Statistik och dataanalys I, 15 hp

Inlamningsuppgift 1

Authors

Namn Minhui Zhong

Namn Johanna Selö

Publicerad

September 25, 2023

Warning

Den här inlämningsuppgiften förutsätter att följande paket finns installerade:

  • mosaic

  • dplyr

  • geosphere

  • leaflet

Paket kan installeras via kommandot install.packages('packagename'), där 'packagename' är namnet på paketet, t.ex 'mosaic'.

Introduktion

I den första inlämningsuppgiften ska ni självständigt i grupper om tre analysera ett dataset i programmeringsspråket R. Till skillnad från datorlaborationerna finns det minimalt med kodexempel. Datorlaborationerna går igenom de flesta momenten som behandlas i inlämningsuppgiften, så se till att göra klart dessa innan.


Instruktioner

I denna inlämningsuppgift ska ni analysera ett datamaterial som beskriver ca 500 distrikt i Boston år 1970. Datasetet är en modifierad version1 av originaldata2 som användes i en studie3 där författarna predikterade medianhuspriser i olika distrikt med hjälp av en rad förklaringsvariabler.

Följande variabler finns i datasetet boston_census_data.Rdata (ladda ner), som innehåller 480 observationer. Notera att en observation motsvarar ett distrikt:

  • town: Stadsdel.
  • longitude: Longitud koordinat.
  • latitude: Latitud koordinat.
  • median_home_value: Medianhuspriset (enhet 1K USD).
  • crime_rate: Brott (per 1000 invånare).
  • zoned_25k_p: Andel av stadsdelens bostadsmark ämnad för marklotter större än 25000 kvadratfot.
  • indust_p: Andel tunnland ägd av företag utanför detaljhandel.
  • borders_charles: Charles River dummy variabel (= 1 om området gränsar till floden, 0 annars).
  • NOx: Koncentration av kväveoxider (andelar per 10 miljon).
  • n_rooms_avg: Genomsnitt antal rum i ägda bostäder.
  • before_1940_p: Andel ägda bostäder byggda före 1940.
  • employ_dist: Viktat avstånd till fem arbetsförmedlingscentra i Boston.
  • radial_access: Index som mäter tillgång till stadsmotorvägar.
  • tax_rate: Fastighetsskatt per 10000 USD.
  • pupil_teacher_ratio: Lärartäthet mätt som elev per lärare.
  • lower_stat_pct: Procentandel med låg socioekonomisk status i termer av utbildning eller arbete.
  • dist_fenway_park: Avstånd till stadion Fenway Park.

Inlämningsuppgiften ska lämnas in i form av ett html-dokument genererat av Quarto. Kontrollera att ni inte får några felmeddelande när du genererar HTML-dokumentet. Läs sedan igenom HTML-dokumentet noggrant innan ni lämnar in det. Använd tydliga figurer och namnge axlarna med tydliga variabelnamn. Glöm inte att skriva era namn i början av dokumentet, där det nu står Namn 1, Namn 2 och Namn 3.

0. Ladda in data

💪 Uppgift 0.1

Ladda in datasetet Boston_census_data med följande kod.

Uppgift 0.1 - Svar
load(file = url("https://github.com/StatisticsSU/SDA1/blob/main/assignments/assignment1/Boston_census_data.RData?raw=true")) 
Boston_census <- Boston_census_data
Boston_census
                       town longitude latitude median_home_value crime_rate
1                Somerville  -71.0677  42.2335              17.4    0.32264
2                  Weymouth  -70.9650  42.1503              18.7    0.06151
3        Boston East Boston  -71.0215  42.2270              12.3    7.99248
4       Boston Forest Hills  -71.0511  42.1879              13.3    6.39312
5         Boston Savin Hill  -71.0455  42.1768              14.4    9.51363
6                Burlington  -71.1095  42.3008              21.7    0.15876
7         Boston Savin Hill  -71.0400  42.1770              17.8    8.24809
8         Boston Savin Hill  -71.0445  42.1938               8.4   13.67810
9                 Watertown  -71.1050  42.2235              28.7    0.07013
10                 Pembroke  -70.8530  42.0520              18.2    0.04301
11                Wellesley  -71.1660  42.1870              45.4    0.03578
12                Cambridge  -71.0480  42.2222              13.4    3.32105
13        Boston Savin Hill  -71.0345  42.1850              17.1    9.72418
14          Boston Mattapan  -71.0740  42.1680              19.9    4.34879
15                 Winthrop  -70.9875  42.2240              22.0    0.10959
16        Boston Savin Hill  -71.0495  42.1815              14.3    5.58107
17                     Lynn  -70.9730  42.2790              14.5    0.98843
18                    Salem  -70.9510  42.3060              21.7    0.09378
19  Boston Allston-Brighton  -71.0865  42.2100              19.9    3.83684
20          Boston Downtown  -71.0427  42.2090              27.9   11.95110
21                  Medford  -71.0600  42.2540              19.4    0.26363
22                   Dedham  -71.0982  42.1445              24.4    0.11460
23                   Natick  -71.2055  42.1875              23.7    0.08244
24                Cambridge  -71.0662  42.2162              17.0    1.41385
25               Marshfield  -70.8100  42.0590              18.6    0.07244
26                  Norwell  -70.9200  42.1016              24.5    0.01501
27                  Norwood  -71.1309  42.1166              28.6    0.12932
28      Boston Forest Hills  -71.0670  42.1945              21.4   14.33370
29       Boston East Boston  -71.0200  42.2205               9.7   11.57790
30                  Melrose  -71.0425  42.2715              22.0    0.03932
31                  Peabody  -70.9525  42.3208              19.4    0.21977
32       Boston Charlestown  -71.0460  42.2300              10.4   88.97620
33                Cambridge  -71.0645  42.2150              19.4    2.14918
34                  Medford  -71.0668  42.2545              27.5    0.14866
35      Boston South Boston  -71.0167  42.2010              13.8    8.64476
36                     Lynn  -70.9720  42.2765              13.2    1.38799
37               Somerville  -71.0760  42.2405              15.6    0.97617
38      Boston Forest Hills  -71.0732  42.1840              29.8    4.64689
39        Boston Savin Hill  -71.0428  42.1845              13.0    7.52601
40                Cambridge  -71.0690  42.2285              41.3    1.22358
41                 Weymouth  -70.9650  42.1010              20.7    0.03738
42                 Stoneham  -71.0530  42.2830              22.9    0.04203
43                   Malden  -71.0428  42.2580              18.7    0.22212
44                Wakefield  -71.0390  42.2885              22.2    0.07151
45                   Quincy  -71.0040  42.1425              19.8    0.24522
46                  Belmont  -71.1175  42.2350              29.6    0.06047
47        Boston Dorchester  -71.0475  42.1690              14.9    7.75223
48               Framingham  -71.2475  42.1825              26.2    0.19073
49                   Sharon  -71.1200  42.0725              22.5    0.06466
50                  Needham  -71.1405  42.1632              33.2    0.10469
51                 Rockland  -70.9470  42.0725              17.5    0.03113
52           Boston Roxbury  -71.0520  42.1854              16.1    6.44405
53                   Revere  -71.0125  42.2462              21.8    0.17331
54      Boston Forest Hills  -71.0565  42.1880              16.7    4.87141
55  Boston Allston-Brighton  -71.0950  42.2120              21.7    3.84970
56                  Peabody  -71.0040  42.3350              26.6    0.12744
57                  Hingham  -70.9325  42.1230              31.2    0.03049
58                  Chelsea  -71.0189  42.2344              15.2    0.15086
59                 Winthrop  -70.9860  42.2312              22.4    0.06263
60       Boston Charlestown  -71.0340  42.2260              13.9   15.28800
61                   Newton  -71.1208  42.2183              30.1    0.61470
62                  Waltham  -71.1500  42.2308              24.4    0.22969
63                Cambridge  -71.0519  42.2230              15.6    4.09740
64       Boston East Boston  -71.0195  42.2255              10.2   14.33370
65                     Lynn  -70.9640  42.2840              13.9    0.84054
66                 Pembroke  -70.8525  42.0300              20.6    0.10659
67                  Waltham  -71.1245  42.2277              25.0    0.19802
68                  Peabody  -70.9560  42.3125              16.6    0.22927
69                Cambridge  -71.0620  42.2236              21.5    1.65660
70                     Lynn  -70.9720  42.2870              18.2    0.63796
71       Boston East Boston  -71.0410  42.2290              10.9   15.87440
72                  Chelsea  -71.0228  42.2335               7.0    0.18337
73                Braintree  -71.0100  42.1215              22.2    0.24103
74               Somerville  -71.0750  42.2400              19.6    1.19294
75                   Newton  -71.1320  42.2142              29.0    0.44791
76                Wellesley  -71.1480  42.1880              35.1    0.21038
77                     Lynn  -70.9775  42.2720              13.5    1.61282
78                  Needham  -71.1380  42.1733              32.0    0.09604
79               Burlington  -71.1230  42.2920              23.4    0.19539
80                   Wenham  -70.9295  42.3715              31.6    0.01432
81                Cambridge  -71.0810  42.2368              17.4    1.20742
82           Boston Roxbury  -71.0455  42.1953               7.2   18.08460
83                   Revere  -71.0105  42.2547              23.1    0.17899
84                     Lynn  -70.9670  42.2790              12.7    1.13081
85          Boston Downtown  -71.0455  42.2060              27.5   14.43830
86          Boston Mattapan  -71.0833  42.1750              23.2    3.56868
87           Boston Roxbury  -71.0618  42.1990              16.7   11.08740
88                  Medford  -71.0550  42.2505              19.8    0.12802
89                   Sargus  -71.0200  42.2875              24.2    0.17505
90                   Malden  -71.0285  42.2620              19.2    0.15098
91                  Melrose  -71.0420  42.2796              23.6    0.05660
92                     Lynn  -70.9780  42.2850              17.5    0.78420
93      Boston South Boston  -71.0300  42.1988              12.1    9.59571
94        Boston Savin Hill  -71.0460  42.1810              13.4    6.71772
95           Boston Roxbury  -71.0650  42.2018              14.2    7.02259
96                Brookline  -71.0835  42.2000              48.8    0.52014
97                  Concord  -71.2400  42.2725              30.3    0.04666
98                 Sherborn  -71.2230  42.1450              44.0    0.01538
99        Boston Savin Hill  -71.0510  42.1780              14.1    4.75237
100                 Melrose  -71.0345  42.2785              28.7    0.05302
101                  Natick  -71.2138  42.1645              20.1    0.10612
102         Boston Mattapan  -71.0660  42.1780              19.1    4.42228
103 Boston Allston-Brighton  -71.1007  42.2100              22.7    5.20177
104     Boston Forest Hills  -71.0528  42.1920              12.0   15.02340
105               Brookline  -71.0765  42.2075              30.1    0.65665
106         Boston Downtown  -71.0487  42.2048              17.2   14.05070
107              Marblehead  -70.9280  42.2930              33.4    0.03237
108                 Beverly  -70.9215  42.3320              22.2    0.11027
109                    Lynn  -70.9880  42.2776              18.2    0.72580
110     Boston South Boston  -71.0230  42.2090               5.0   38.35180
111 Boston Allston-Brighton  -71.0930  42.2070              22.6    4.26131
112         Boston Back Bay  -71.0595  42.2075              27.5    4.55587
113                 Duxbury  -70.8300  42.0485              30.1    0.01709
114                  Newton  -71.1285  42.1930              31.7    0.46296
115              Framingham  -71.2550  42.1767              24.5    0.16439
116                 Belmont  -71.1000  42.2408              37.2    0.05780
117                Stoneham  -71.0620  42.2960              25.0    0.02875
118               Cambridge  -71.0555  42.2222              14.6    2.36862
119       Boston Dorchester  -71.0430  42.1728              16.4    4.81213
120               Braintree  -70.9834  42.1375              18.5    0.28392
121          Boston Roxbury  -71.0505  42.1880              14.1   10.06230
122                    Lynn  -70.9597  42.2870              16.6    0.67191
123                  Woburn  -71.0910  42.3050              20.3    0.08387
124                Winthrop  -70.9825  42.2210              19.0    0.04741
125                 Waltham  -71.1375  42.2355              28.1    0.14052
126                  Quincy  -71.0138  42.1555              22.8    0.49298
127                  Malden  -71.0285  42.2580              20.4    0.13058
128                  Revere  -70.9920  42.2380              16.8    0.22438
129 Boston Allston-Brighton  -71.0905  42.2033              25.0    4.54192
130                    Lynn  -70.9693  42.2816              15.6    0.75026
131              Winchester  -71.0800  42.2680              33.2    0.06860
132                 Beverly  -70.9385  42.3460              23.3    0.15445
133                  Quincy  -71.0150  42.1670              19.4    0.26169
134                 Danvers  -70.9510  42.3340              19.7    0.08873
135                 Walpole  -71.1325  42.0940              22.3    0.04590
136         Boston Downtown  -71.0390  42.2198              11.9   20.71620
137 Boston Allston-Brighton  -71.0865  42.2150              16.8    4.22239
138                  Dedham  -71.0940  42.1355              25.2    0.16211
139               Lynnfield  -71.0130  42.3130              30.8    0.02763
140         Boston Back Bay  -71.0590  42.2098              21.9    3.47428
141                 Waltham  -71.1435  42.2177              21.7    0.17446
142               Cambridge  -71.0650  42.2223              23.3    1.42502
143              Wilmington  -71.0900  42.3362              22.0    0.05789
144                Westwood  -71.1385  42.1235              28.5    0.03502
145                  Malden  -71.0360  42.2608              21.2    0.13158
146                Winthrop  -70.9910  42.2275              20.6    0.04527
147               Arlington  -71.1125  42.2550              23.2    0.07022
148       Boston Savin Hill  -71.0445  42.1917               8.2   15.17720
149               Cambridge  -71.0510  42.2205              11.8    2.77974
150                  Quincy  -71.0201  42.1600              20.3    0.34940
151                Westwood  -71.1330  42.1408              37.3    0.07886
152              Somerville  -71.0580  42.2350              18.0    0.32543
153       Boston Savin Hill  -71.0410  42.1795              15.2    5.44114
154              Somerville  -71.0543  42.2265              14.4    1.62864
155                 Everett  -71.0370  42.2435              17.3    0.15038
156          Boston Roxbury  -71.0525  42.1989               8.8   73.53410
157                 Medford  -71.0810  42.2450              26.5    0.11432
158              Framingham  -71.2685  42.1935              29.6    0.08221
159                Holbrook  -70.9960  42.0895              19.4    0.03466
160     Boston Forest Hills  -71.0558  42.1913              14.6   10.23300
161                  Quincy  -70.9795  42.1580              16.2    0.25356
162                 Norwood  -71.1180  42.1217              21.7    0.08199
163                 Peabody  -70.9550  42.3165              14.4    0.25387
164     Boston South Boston  -71.0300  42.2015               7.2   14.23620
165               Cambridge  -71.0680  42.2150              15.6    3.53501
166       Boston Dorchester  -71.0550  42.1685              19.0    3.77498
167                  Newton  -71.1491  42.2030              31.5    0.51183
168       Boston Savin Hill  -71.0321  42.1925              10.5   22.05110
169                 Norwood  -71.1090  42.1100              23.9    0.08265
170                 Beverly  -70.9400  42.3320              19.6    0.10328
171                 Waltham  -71.1335  42.2250              22.4    0.21719
172                  Newton  -71.1215  42.2025              37.6    0.38214
173                 Beverly  -70.9075  42.3390              25.0    0.12650
174      Boston Charlestown  -71.0400  42.2248              13.1   23.64820
175              Somerville  -71.0745  42.2405              23.0    0.59005
176                 Belmont  -71.0966  42.2282              36.2    0.06888
177              Marshfield  -70.8300  42.0775              24.1    0.07950
178                    Lynn  -70.9645  42.2920              20.4    0.62976
179              Wilmington  -71.1080  42.3400              17.4    0.13554
180              Wilmington  -71.1110  42.3270              20.9    0.12816
181         Boston Mattapan  -71.0825  42.1698              19.6    4.03841
182                Stoneham  -71.0615  42.2840              20.6    0.04294
183               Cambridge  -71.0567  42.2240              17.8    2.33099
184                 Sudbury  -71.2630  42.2225              32.9    0.01778
185          Boston Roxbury  -71.0665  42.1970              20.8   12.04820
186                   Salem  -70.9375  42.3100              22.1    0.14455
187                  Newton  -71.1160  42.1947              31.6    0.41238
188                 Norwood  -71.1280  42.1108              27.1    0.05372
189               Watertown  -71.1060  42.2185              23.0    0.11425
190                Weymouth  -70.9675  42.1440              19.0    0.05497
191     Boston South Boston  -71.0345  42.2001               8.5   41.52920
192                    Lynn  -70.9820  42.2810              19.6    0.85204
193               Cambridge  -71.0670  42.2245              24.3    1.34284
194       Boston Savin Hill  -71.0370  42.1940              12.8    9.39063
195                  Canton  -71.0875  42.0950              22.0    0.03537
196               Cambridge  -71.0622  42.2205              19.6    1.49632
197              Burlington  -71.1210  42.3160              24.2    0.08826
198      Boston East Boston  -71.0245  42.2235               8.8   20.08490
199                 Concord  -71.2200  42.2715              33.3    0.04011
200              Somerville  -71.0790  42.2450              18.4    0.32982
201          Boston Roxbury  -71.0577  42.1967               8.3   15.86030
202     Boston South Boston  -71.0330  42.2032               6.3    9.91655
203                  Newton  -71.1400  42.1946              41.7    0.57529
204     Boston South Boston  -71.0200  42.1993              12.7   13.35980
205                 Belmont  -71.1120  42.2300              26.4    0.08308
206                 Danvers  -70.9580  42.3460              25.0    0.05360
207              Winchester  -71.0760  42.2775              28.4    0.12204
208                 Medford  -71.0662  42.2425              19.5    0.13262
209                 Hingham  -70.9370  42.1475              23.9    0.02543
210                  Newton  -71.1300  42.1880              24.3    0.53700
211                  Newton  -71.1210  42.2166              21.7    0.40771
212                    Lynn  -70.9640  42.2765              14.5    1.35472
213                 Chelsea  -71.0160  42.2382              13.6    0.10574
214          Boston Roxbury  -71.0547  42.1890              14.5    8.49213
215                   Salem  -70.9440  42.3170              18.9    0.11747
216                Scituate  -70.8330  42.1150              22.9    0.06211
217                  Canton  -71.0625  42.1020              26.4    0.09266
218               Braintree  -70.9995  42.1175              23.0    0.30347
219               Cambridge  -71.0590  42.2170              15.3    1.12658
220              Somerville  -71.0620  42.2275              13.3    0.24980
221          Boston Roxbury  -71.0485  42.1920               9.5    9.33889
222                 Needham  -71.1395  42.1813              29.1    0.07978
223       Boston Dorchester  -71.0450  42.1640              21.4    7.83932
224       Boston Dorchester  -71.0550  42.1650              19.9    3.16360
225              Winchester  -71.0890  42.2715              38.7    0.12083
226              Manchester  -70.8600  42.3450              33.0    0.01951
227     Boston West Roxbury  -71.0950  42.1730              23.7    5.70818
228     Boston West Roxbury  -71.0975  42.1608              21.8    2.81838
229               Brookline  -71.0925  42.2075              43.5    0.54050
230         Boston Downtown  -71.0462  42.2075              15.0   51.13580
231     Boston West Roxbury  -71.1008  42.1740              23.0    5.82401
232               Cambridge  -71.0590  42.2210              15.6    2.15505
233       Boston Savin Hill  -71.0425  42.1890              11.8   10.67180
234                  Weston  -71.1990  42.2320              48.5    0.03510
235               Cambridge  -71.0775  42.2351              22.3    2.44953
236                Randolph  -71.0275  42.1130              19.3    0.06617
237                 Beverly  -70.9300  42.3275              16.0    0.17171
238                 Peabody  -70.9650  42.3075              20.0    0.18836
239       Boston Dorchester  -71.0515  42.1700              13.5    8.20058
240               Arlington  -71.0855  42.2450              23.6    0.09178
241              Framingham  -71.2575  42.1618              18.5    0.19133
242        Boston Hyde Park  -71.0650  42.1610              20.6    4.83567
243                  Dedham  -71.0980  42.1540              20.7    0.09065
244                 Belmont  -71.0995  42.2345              39.8    0.06588
245                  Sargus  -71.0000  42.2700              18.9    0.06417
246                  Newton  -71.1100  42.2137              26.7    0.35809
247                  Malden  -71.0396  42.2512              18.5    0.14231
248                Weymouth  -70.9602  42.1270              18.5    0.03041
249                 Peabody  -71.0030  42.3235              25.3    0.14150
250                    Lynn  -70.9597  42.2825              14.8    0.95577
251      Boston Charlestown  -71.0400  42.2275              10.2   17.86670
252               Lexington  -71.1450  42.2651              34.9    0.08370
253       Boston Dorchester  -71.0430  42.1690              20.0    6.80117
254                 Danvers  -70.9630  42.3382              20.5    0.04337
255       Boston Savin Hill  -71.0475  42.1842              11.7   13.91340
256                    Lynn  -70.9510  42.2780              21.0    1.00245
257               Arlington  -71.0965  42.2470              29.9    0.06642
258     Boston South Boston  -71.0260  42.1993              12.5    5.87205
259               Brookline  -71.0800  42.2040              33.8    0.54011
260               Brookline  -71.0750  42.1980              31.0    0.82526
261              Framingham  -71.2380  42.1910              24.4    0.14030
262      Boston Charlestown  -71.0367  42.2240              15.0   19.60910
263                 Ashland  -71.2895  42.1575              21.9    0.04819
264              Burlington  -71.1300  42.3050              22.8    0.09164
265                  Malden  -71.0355  42.2545              18.3    0.17134
266          Boston Roxbury  -71.0420  42.1985               7.0   45.74610
267                 Beverly  -70.9300  42.3370              18.7    0.14932
268      Boston East Boston  -71.0230  42.2287              11.3    9.18702
269        Boston Hyde Park  -71.0750  42.1455              21.2    3.67367
270                   Salem  -70.9290  42.3160              18.9    0.17004
271       Boston Savin Hill  -71.0455  42.1893               9.6   14.42080
272                Randolph  -71.0415  42.1150              22.6    0.06724
273                  Woburn  -71.0900  42.2835              20.0    0.10153
274      Boston East Boston  -71.0228  42.2231              10.5   24.39380
275                Scituate  -70.8550  42.1300              26.6    0.02899
276        Boston Hyde Park  -71.0715  42.1550              19.1    5.69175
277         Boston Downtown  -71.0451  42.2015              16.3   28.65580
278                  Sharon  -71.1000  42.0590              29.0    0.05561
279               Lexington  -71.1340  42.2785              36.4    0.08664
280                  Revere  -70.9947  42.2496              18.3    0.26838
281       Boston Savin Hill  -71.0390  42.1868              14.9    6.28807
282          Boston Roxbury  -71.0477  42.1965               7.5   10.83420
283       Boston Savin Hill  -71.0400  42.1820              14.1    9.32909
284                  Natick  -71.2320  42.1725              23.7    0.12757
285               Wakefield  -71.0500  42.3000              26.6    0.05735
286                Westwood  -71.1070  42.1307              27.9    0.03615
287     Boston Forest Hills  -71.0550  42.1830              13.8    8.05579
288                 Reading  -71.0675  42.3260              24.8    0.03659
289         Boston Mattapan  -71.0690  42.1725              20.1   13.07510
290               Cambridge  -71.0866  42.2345              23.8    1.80028
291                  Canton  -71.0865  42.1200              33.1    0.10000
292      Boston East Boston  -71.0109  42.2300              15.1    6.96215
293                  Woburn  -71.0905  42.2950              21.2    0.05646
294                 Everett  -71.0262  42.2431              21.4    0.16902
295                  Revere  -71.0050  42.2455              21.2    0.23912
296               Middleton  -71.0175  42.3715              18.9    0.01360
297                 Peabody  -70.9725  42.3075              19.3    0.17142
298       Boston Savin Hill  -71.0340  42.1890              14.8    5.66637
299                 Medford  -71.0622  42.2431              19.5    0.17120
300                 Sudbury  -71.2440  42.2425              34.9    0.03150
301                 Everett  -71.0377  42.2470              20.5    0.09299
302                  Revere  -71.0125  42.2500              24.5    0.27957
303                 Bedford  -71.1525  42.3000              31.1    0.02187
304                 Medford  -71.0690  42.2480              20.1    0.13960
305          Boston Roxbury  -71.0590  42.1920              11.7    8.79212
306        Boston North End  -71.0339  42.2207              13.8   11.10810
307                  Malden  -71.0490  42.2530              18.8    0.12329
308       Boston Dorchester  -71.0358  42.1675              20.2    5.82115
309                 Walpole  -71.1550  42.0980              24.8    0.04297
310              Somerville  -71.0530  42.2355              16.2    0.25915
311               Cambridge  -71.0792  42.2390              19.1    2.31390
312           North Reading  -71.0690  42.3525              19.4    0.04379
313               Arlington  -71.1060  42.2512              24.6    0.05425
314                  Quincy  -71.0100  42.1500              23.1    0.40202
315                  Quincy  -71.0000  42.1530              23.8    0.36920
316                 Peabody  -70.9775  42.3237              24.7    0.15936
317                Weymouth  -70.9760  42.1280              19.5    0.03427
318                 Chelsea  -71.0245  42.2368               8.1    0.20746
319                  Quincy  -71.0075  42.1613              21.6    0.26938
320                 Chelsea  -71.0297  42.2447              20.1    0.11132
321               Arlington  -71.0833  42.2475              22.6    0.08447
322                    Lynn  -70.9925  42.2825              20.2    0.80271
323                 Norwood  -71.1210  42.1025              20.3    0.14103
324                Hamilton  -70.9300  42.3740              24.7    0.02055
325                 Walpole  -71.1480  42.0775              23.2    0.03871
326          Boston Roxbury  -71.0558  42.1937              10.2   12.24720
327          Boston Roxbury  -71.0586  42.1999               8.4   11.81230
328                 Needham  -71.1495  42.1730              33.1    0.06127
329                 Bedford  -71.1633  42.3030              29.1    0.01439
330      Boston Charlestown  -71.0380  42.2265              13.3    9.82349
331                    Hull  -70.9150  42.1600              16.5    0.02498
332                  Milton  -71.0280  42.1565              28.2    0.04932
333     Boston South Boston  -71.0250  42.2024               8.5    7.67202
334                  Malden  -71.0190  42.2605              19.3    0.14476
335     Boston South Boston  -71.0220  42.1996              13.1    8.71675
336              Somerville  -71.0692  42.2390              19.2    0.34006
337              Framingham  -71.2435  42.1630              17.6    0.20608
338          Boston Roxbury  -71.0542  42.1961              10.9   37.66190
339              Marblehead  -70.9220  42.2980              36.2    0.06905
340                 Everett  -71.0308  42.2450              18.8    0.09849
341                  Newton  -71.1485  42.2110              25.1    0.52058
342               Brookline  -71.0710  42.2030              36.5    0.55007
343               Wakefield  -71.0430  42.3075              23.9    0.05059
344               Cambridge  -71.0918  42.2265              22.7    2.24236
345               Watertown  -71.1166  42.2230              23.3    0.04560
346       Boston Savin Hill  -71.0370  42.1840              12.6    9.92485
347                  Quincy  -71.0075  42.1780              22.1    0.79041
348     Boston South Boston  -71.0326  42.2011               5.6   25.04610
349               Topsfield  -70.9625  42.3810              35.4    0.01311
350          Boston Roxbury  -71.0619  42.1948              13.4    7.05042
351               Lexington  -71.1408  42.2550              29.8    0.12579
352              Marblehead  -70.9165  42.3040              28.7    0.02985
353                 Medford  -71.0770  42.2490              19.3    0.21161
354      Boston East Boston  -71.0035  42.2330              23.2    5.29305
355               Cambridge  -71.0580  42.2230              15.4    2.73397
356                  Newton  -71.1380  42.2141              24.0    0.33045
357                    Lynn  -70.9795  42.2760              13.1    1.15172
358                   Salem  -70.9360  42.2970              22.9    0.08829
359                 Everett  -71.0333  42.2395              15.7    0.38735
360                 Peabody  -70.9675  42.3170              21.2    0.12269
361               Brookline  -71.0725  42.1965              30.7    0.78570
362                 Waltham  -71.1490  42.2268              22.5    0.25199
363                 Belmont  -71.1005  42.2287              37.9    0.09103
364                  Millis  -71.2135  42.1000              22.0    0.01096
365               Brookline  -71.0727  42.2077              36.0    0.66351
366              Winchester  -71.0982  42.2685              43.8    0.08187
367                 Wayland  -71.2185  42.1955              24.1    0.03445
368                    Lynn  -70.9870  42.2985              23.1    1.05393
369           North Reading  -71.0450  42.3450              23.5    0.03584
370                  Sargus  -71.0080  42.2745              20.0    0.09744
371       Boston Dorchester  -71.0350  42.1745              17.7    3.69311
372                Medfield  -71.1800  42.1105              32.2    0.00906
373                   Salem  -70.9350  42.3160              15.0    0.22489
374               Lynnfield  -71.0300  42.3240              34.9    0.03359
375               Wellesley  -71.1775  42.1735              46.0    0.06129
376 Boston Allston-Brighton  -71.0810  42.2080              20.8    3.67822
377                  Newton  -71.1100  42.2060              44.8    0.31533
378               Brookline  -71.0700  42.2000              22.8    0.76162
379 Boston Allston-Brighton  -71.0830  42.2172              17.8    8.98296
380              Framingham  -71.2470  42.1703              20.5    0.19657
381                 Everett  -71.0243  42.2483              22.0    0.06899
382       Boston Savin Hill  -71.0405  42.1920              10.8   12.80230
383              Framingham  -71.2807  42.1727              42.8    0.36894
384     Boston South Boston  -71.0320  42.2057               5.0   67.92080
385               Arlington  -71.0940  42.2575              29.4    0.06664
386                  Quincy  -70.9880  42.1485              17.8    0.31827
387                  Natick  -71.2035  42.1870              23.3    0.09252
388              Framingham  -71.2435  42.1982              24.8    0.21409
389                  Revere  -71.0010  42.2525              19.7    0.28960
390              Framingham  -71.2620  42.1690              24.3    0.33983
391                    Lynn  -70.9765  42.2940              19.9    0.62739
392                    Lynn  -70.9835  42.2770              13.6    1.25179
393                Holbrook  -71.0115  42.0865              17.1    0.05023
394       Boston Dorchester  -71.0310  42.1695              19.5    6.65492
395      Boston East Boston  -71.0168  42.2281              11.5    8.15174
396               Lexington  -71.1220  42.2565              32.0    0.07875
397                 Waltham  -71.1475  42.2445              22.6    0.13642
398                 Melrose  -71.0300  42.2720              22.6    0.04684
399                  Malden  -71.0475  42.2610              22.8    0.10084
400               Cambridge  -71.0820  42.2295              25.0    2.92400
401                 Concord  -71.2220  42.2890              34.6    0.03768
402       Boston Savin Hill  -71.0378  42.1892              15.4    9.96654
403               Cambridge  -71.0700  42.2214              27.0    1.27346
404               Arlington  -71.0870  42.2416              23.1    0.13914
405               Cambridge  -71.0667  42.2200              13.1    2.44668
406               Braintree  -70.9895  42.1265              25.0    0.34109
407               Braintree  -70.9975  42.1340              23.1    0.18159
408              Swampscott  -70.9360  42.2830              34.7    0.02729
409         Boston Mattapan  -71.0700  42.1680              19.1   15.57570
410              Swampscott  -70.9500  42.2875              21.6    0.02731
411          Boston Roxbury  -71.0521  42.1940              11.0    7.36711
412                 Waltham  -71.1270  42.2350              23.7    0.28955
413                  Dedham  -71.1170  42.1510              35.2    0.22188
414                  Milton  -71.0570  42.1525              28.4    0.05479
415                    Lynn  -70.9775  42.2790              15.2    1.23247
416               Brookline  -71.0790  42.2020              43.1    0.53412
417         Boston Back Bay  -71.0540  42.2052              21.9    3.69695
418               Wakefield  -71.0330  42.3050              22.5    0.05188
419        Boston Hyde Park  -71.0804  42.1540              20.6    2.37857
420         Boston Downtown  -71.0470  42.2030              17.9   18.81100
421                 Medford  -71.0553  42.2465              20.4    0.13117
422        Boston North End  -71.0346  42.2187              13.8   18.49820
423                 Waltham  -71.1380  42.2216              19.3    0.37578
424                  Revere  -70.9985  42.2430              17.5    0.17783
425                  Woburn  -71.1105  42.2890              24.1    0.07896
426                Rockland  -70.9501  42.0825              17.2    0.06162
427              Somerville  -71.0638  42.2368              14.3    0.88125
428         Boston Back Bay  -71.0508  42.2070              23.1   13.52220
429              Somerville  -71.0518  42.2312              14.0    0.29090
430               Watertown  -71.0933  42.2220              21.5    0.11069
431          Boston Roxbury  -71.0498  42.2007              10.4   25.94060
432                 Waltham  -71.1430  42.2217              20.0    0.43571
433                    Lynn  -70.9570  42.2800              18.4    0.77299
434                  Sharon  -71.1035  42.0735              24.8    0.04417
435     Boston West Roxbury  -71.0900  42.1665              25.0    5.73116
436                 Needham  -71.1305  42.1675              32.4    0.05644
437               Lexington  -71.1216  42.2700              33.0    0.09068
438                  Newton  -71.1190  42.1807              31.5    0.44178
439               Cambridge  -71.0540  42.2190              13.8    2.37934
440                  Milton  -71.0450  42.1590              33.4    0.07503
441                Cohasset  -70.8875  42.1465              32.7    0.01301
442              Somerville  -71.0568  42.2300              17.8    0.54452
443              Somerville  -71.0750  42.2362              18.1    0.55778
444                  Woburn  -71.0760  42.2895              20.8    0.08707
445              Winchester  -71.0850  42.2775              21.4    0.11504
446                  Newton  -71.1340  42.2040              48.3    0.33147
447       Boston Dorchester  -71.0517  42.1735              12.7    4.66883
448                  Quincy  -71.0160  42.1760              16.1    2.63548
449               Braintree  -71.0085  42.1290              23.8    0.16760
450                 Medford  -71.0560  42.2605              21.7    0.10793
451                  Nahant  -70.9550  42.2550              24.0    0.00632
452       Boston Savin Hill  -71.0340  42.1790              16.1    5.09017
453                Weymouth  -70.9633  42.1374              20.6    0.03306
454                 Medford  -71.0812  42.2515              18.6    0.22876
455                Weymouth  -70.9700  42.1150              21.1    0.03961
456               Wellesley  -71.1850  42.1848              35.4    0.03705
457              Somerville  -71.0630  42.2325              17.1    0.35233
458               Braintree  -70.9900  42.1367              20.4    0.35114
459                  Woburn  -71.1000  42.2875              21.4    0.09512
460      Boston East Boston  -71.0215  42.2248               7.4   22.59710
461                  Sargus  -71.0040  42.2865              21.0    0.08014
462                 Reading  -71.0575  42.3170              22.9    0.03551
463                 Reading  -71.0690  42.3150              23.9    0.04462
464                  Natick  -71.2200  42.1782              22.2    0.10290
465                  Dedham  -71.0870  42.1410              21.1    0.29916
466         Boston Downtown  -71.0437  42.2050              17.2    7.40389
467      Boston East Boston  -71.0235  42.2213               7.2   16.81180
468               Braintree  -71.0000  42.1066              24.6    0.19186
469                 Everett  -71.0312  42.2505              20.3    0.07165
470                  Newton  -71.1100  42.1850              46.7    0.29819
471                 Ashland  -71.2690  42.1482              20.9    0.03548
472       Boston Savin Hill  -71.0460  42.1867              13.4   11.16040
473                 Hanover  -70.9275  42.0795              23.1    0.01870
474                  Newton  -71.1250  42.2134              27.5    0.62356
475                 Reading  -71.0685  42.3080              28.0    0.04113
476               Cambridge  -71.0740  42.2331              23.8    2.30040
477                 Belmont  -71.1065  42.2300              32.5    0.10008
478                Winthrop  -70.9948  42.2260              23.9    0.06076
479                 Waltham  -71.1503  42.2220              24.4    0.13587
480                 Danvers  -70.9780  42.3425              23.4    0.04981
    zoned_25k_p indust_p borders_charles    NOx n_rooms_avg before_1940_p
1           0.0    21.89               0 0.6240       5.942          93.5
2           0.0     5.19               0 0.5150       5.968          58.5
3           0.0    18.10               0 0.7000       5.520         100.0
4           0.0    18.10               0 0.5840       6.162          97.4
5           0.0    18.10               0 0.7130       6.728          94.1
6           0.0    10.81               0 0.4130       5.961          17.5
7           0.0    18.10               0 0.7130       7.393          99.3
8           0.0    18.10               0 0.7400       5.935          87.9
9           0.0    13.89               0 0.5500       6.642          85.1
10         80.0     1.91               0 0.4130       5.663          21.9
11         20.0     3.33               0 0.4429       7.820          64.5
12          0.0    19.58               1 0.8710       5.403         100.0
13          0.0    18.10               0 0.7400       6.406          97.2
14          0.0    18.10               0 0.5800       6.167          84.0
15          0.0    11.93               0 0.5730       6.794          89.3
16          0.0    18.10               0 0.7130       6.436          87.9
17          0.0     8.14               0 0.5380       5.813         100.0
18         12.5     7.87               0 0.5240       5.889          39.0
19          0.0    18.10               0 0.7700       6.251          91.1
20          0.0    18.10               0 0.6590       5.608         100.0
21          0.0     8.56               0 0.5200       6.229          91.2
22         20.0     6.96               0 0.4640       6.538          58.7
23         30.0     4.93               0 0.4280       6.481          18.5
24          0.0    19.58               1 0.8710       6.129          96.0
25         60.0     1.69               0 0.4110       5.884          18.5
26         80.0     2.01               0 0.4350       6.635          29.7
27          0.0    13.92               0 0.4370       6.678          31.1
28          0.0    18.10               0 0.6140       6.229          88.0
29          0.0    18.10               0 0.7000       5.036          97.0
30          0.0     3.41               0 0.4890       6.405          73.9
31          0.0     6.91               0 0.4480       5.602          62.0
32          0.0    18.10               0 0.6710       6.968          91.9
33          0.0    19.58               0 0.8710       5.709          98.5
34          0.0     8.56               0 0.5200       6.727          79.9
35          0.0    18.10               0 0.6930       6.193          92.6
36          0.0     8.14               0 0.5380       5.950          82.0
37          0.0    21.89               0 0.6240       5.757          98.4
38          0.0    18.10               0 0.6140       6.980          67.6
39          0.0    18.10               0 0.7130       6.417          98.3
40          0.0    19.58               0 0.6050       6.943          97.4
41          0.0     5.19               0 0.5150       6.310          38.5
42         28.0    15.04               0 0.4640       6.442          53.6
43          0.0    10.01               0 0.5470       6.092          95.4
44          0.0     4.49               0 0.4490       6.121          56.8
45          0.0     9.90               0 0.5440       5.782          71.7
46          0.0     2.46               0 0.4880       6.153          68.8
47          0.0    18.10               0 0.7130       6.301          83.7
48         22.0     5.86               0 0.4310       6.718          17.5
49         70.0     2.24               0 0.4000       6.345          20.1
50         40.0     6.41               1 0.4470       7.267          49.0
51          0.0     4.39               0 0.4420       6.014          48.5
52          0.0    18.10               0 0.5840       6.425          74.8
53          0.0     9.69               0 0.5850       5.707          54.0
54          0.0    18.10               0 0.6140       6.484          93.6
55          0.0    18.10               1 0.7700       6.395          91.0
56          0.0     6.91               0 0.4480       6.770           2.9
57         55.0     3.78               0 0.4840       6.874          28.1
58          0.0    27.74               0 0.6090       5.454          92.7
59          0.0    11.93               0 0.5730       6.593          69.1
60          0.0    18.10               0 0.6710       6.649          93.3
61          0.0     6.20               0 0.5070       6.618          80.8
62          0.0    10.59               0 0.4890       6.326          52.5
63          0.0    19.58               0 0.8710       5.468         100.0
64          0.0    18.10               0 0.7000       4.880         100.0
65          0.0     8.14               0 0.5380       5.599          85.7
66         80.0     1.91               0 0.4130       5.936          19.5
67          0.0    10.59               0 0.4890       6.182          42.4
68          0.0     6.91               0 0.4480       6.030          85.5
69          0.0    19.58               0 0.8710       6.122          97.3
70          0.0     8.14               0 0.5380       6.096          84.5
71          0.0    18.10               0 0.6710       6.545          99.1
72          0.0    27.74               0 0.6090       5.414          98.3
73          0.0     7.38               0 0.4930       6.083          43.7
74          0.0    21.89               0 0.6240       6.326          97.7
75          0.0     6.20               1 0.5070       6.726          66.5
76         20.0     3.33               0 0.4429       6.812          32.2
77          0.0     8.14               0 0.5380       6.096          96.9
78         40.0     6.41               0 0.4470       6.854          42.8
79          0.0    10.81               0 0.4130       6.245           6.2
80        100.0     1.32               0 0.4110       6.816          40.5
81          0.0    19.58               0 0.6050       5.875          94.6
82          0.0    18.10               0 0.6790       6.434         100.0
83          0.0     9.69               0 0.5850       5.670          28.8
84          0.0     8.14               0 0.5380       5.713          94.1
85          0.0    18.10               0 0.5970       6.852         100.0
86          0.0    18.10               0 0.5800       6.437          75.0
87          0.0    18.10               0 0.7180       6.411         100.0
88          0.0     8.56               0 0.5200       6.474          97.1
89          0.0     5.96               0 0.4990       5.966          30.2
90          0.0    10.01               0 0.5470       6.021          82.6
91          0.0     3.41               0 0.4890       7.007          86.3
92          0.0     8.14               0 0.5380       5.990          81.7
93          0.0    18.10               0 0.6930       6.404         100.0
94          0.0    18.10               0 0.7130       6.749          92.6
95          0.0    18.10               0 0.7180       6.006          95.3
96         20.0     3.97               0 0.6470       8.398          91.5
97         80.0     1.52               0 0.4040       7.107          36.6
98         90.0     3.75               0 0.3940       7.454          34.2
99          0.0    18.10               0 0.7130       6.525          86.5
100         0.0     3.41               0 0.4890       7.079          63.1
101        30.0     4.93               0 0.4280       6.095          65.1
102         0.0    18.10               0 0.5840       6.003          94.5
103         0.0    18.10               1 0.7700       6.127          83.4
104         0.0    18.10               0 0.6140       5.304          97.3
105        20.0     3.97               0 0.6470       6.842         100.0
106         0.0    18.10               0 0.5970       6.657         100.0
107         0.0     2.18               0 0.4580       6.998          45.8
108        25.0     5.13               0 0.4530       6.456          67.8
109         0.0     8.14               0 0.5380       5.727          69.5
110         0.0    18.10               0 0.6930       5.453         100.0
111         0.0    18.10               0 0.7700       6.112          81.3
112         0.0    18.10               0 0.7180       3.561          87.9
113        90.0     2.02               0 0.4100       6.728          36.1
114         0.0     6.20               0 0.5040       7.412          76.9
115        22.0     5.86               0 0.4310       6.433          49.1
116         0.0     2.46               0 0.4880       6.980          58.4
117        28.0    15.04               0 0.4640       6.211          28.9
118         0.0    19.58               0 0.8710       4.926          95.7
119         0.0    18.10               0 0.7130       6.701          90.0
120         0.0     7.38               0 0.4930       5.708          74.3
121         0.0    18.10               0 0.5840       6.833          94.3
122         0.0     8.14               0 0.5380       5.813          90.3
123         0.0    12.83               0 0.4370       5.874          36.6
124         0.0    11.93               0 0.5730       6.030          80.8
125         0.0    10.59               0 0.4890       6.375          32.3
126         0.0     9.90               0 0.5440       6.635          82.5
127         0.0    10.01               0 0.5470       5.872          73.1
128         0.0     9.69               0 0.5850       6.027          79.7
129         0.0    18.10               0 0.7700       6.398          88.0
130         0.0     8.14               0 0.5380       5.924          94.1
131         0.0     2.89               0 0.4450       7.416          62.5
132        25.0     5.13               0 0.4530       6.145          29.2
133         0.0     9.90               0 0.5440       6.023          90.4
134        21.0     5.64               0 0.4390       5.963          45.7
135        52.5     5.32               0 0.4050       6.315          45.6
136         0.0    18.10               0 0.6590       4.138         100.0
137         0.0    18.10               1 0.7700       5.803          89.0
138        20.0     6.96               0 0.4640       6.240          16.3
139        75.0     2.95               0 0.4280       6.595          21.8
140         0.0    18.10               1 0.7180       8.780          82.9
141         0.0    10.59               1 0.4890       5.960          92.1
142         0.0    19.58               0 0.8710       6.510         100.0
143        12.5     6.07               0 0.4090       5.878          21.4
144        80.0     4.95               0 0.4110       6.861          27.9
145         0.0    10.01               0 0.5470       6.176          72.5
146         0.0    11.93               0 0.5730       6.120          76.7
147         0.0     4.05               0 0.5100       6.020          47.2
148         0.0    18.10               0 0.7400       6.152         100.0
149         0.0    19.58               0 0.8710       4.903          97.8
150         0.0     9.90               0 0.5440       5.972          76.7
151        80.0     4.95               0 0.4110       7.148          27.7
152         0.0    21.89               0 0.6240       6.431          98.8
153         0.0    18.10               0 0.7130       6.655          98.2
154         0.0    21.89               0 0.6240       5.019         100.0
155         0.0    25.65               0 0.5810       5.856          97.0
156         0.0    18.10               0 0.6790       5.957         100.0
157         0.0     8.56               0 0.5200       6.781          71.3
158        22.0     5.86               0 0.4310       6.957           6.8
159        35.0     6.06               0 0.4379       6.031          23.3
160         0.0    18.10               0 0.6140       6.185          96.7
161         0.0     9.90               0 0.5440       5.705          77.7
162         0.0    13.92               0 0.4370       6.009          42.3
163         0.0     6.91               0 0.4480       5.399          95.3
164         0.0    18.10               0 0.6930       6.343         100.0
165         0.0    19.58               1 0.8710       6.152          82.6
166         0.0    18.10               0 0.6550       5.952          84.7
167         0.0     6.20               0 0.5070       7.358          71.6
168         0.0    18.10               0 0.7400       5.818          92.4
169         0.0    13.92               0 0.4370       6.127          18.4
170        25.0     5.13               0 0.4530       5.927          47.2
171         0.0    10.59               1 0.4890       5.807          53.8
172         0.0     6.20               0 0.5040       8.040          86.5
173        25.0     5.13               0 0.4530       6.762          43.4
174         0.0    18.10               0 0.6710       6.380          96.2
175         0.0    21.89               0 0.6240       6.372          97.9
176         0.0     2.46               0 0.4880       6.144          62.2
177        60.0     1.69               0 0.4110       6.579          35.9
178         0.0     8.14               0 0.5380       5.949          61.8
179        12.5     6.07               0 0.4090       5.594          36.8
180        12.5     6.07               0 0.4090       5.885          33.0
181         0.0    18.10               0 0.5320       6.229          90.7
182        28.0    15.04               0 0.4640       6.249          77.3
183         0.0    19.58               0 0.8710       5.186          93.8
184        95.0     1.47               0 0.4030       7.135          13.9
185         0.0    18.10               0 0.6140       5.648          87.6
186        12.5     7.87               0 0.5240       6.172          96.1
187         0.0     6.20               0 0.5040       7.163          79.9
188         0.0    13.92               0 0.4370       6.549          51.0
189         0.0    13.89               1 0.5500       6.373          92.4
190         0.0     5.19               0 0.5150       5.985          45.4
191         0.0    18.10               0 0.6930       5.531          85.4
192         0.0     8.14               0 0.5380       5.965          89.2
193         0.0    19.58               0 0.6050       6.066         100.0
194         0.0    18.10               0 0.7400       5.627          93.9
195        34.0     6.09               0 0.4330       6.590          40.4
196         0.0    19.58               0 0.8710       5.404         100.0
197         0.0    10.81               0 0.4130       6.417           6.6
198         0.0    18.10               0 0.7000       4.368          91.2
199        80.0     1.52               0 0.4040       7.287          34.1
200         0.0    21.89               0 0.6240       5.822          95.4
201         0.0    18.10               0 0.6790       5.896          95.4
202         0.0    18.10               0 0.6930       5.852          77.8
203         0.0     6.20               0 0.5070       8.337          73.3
204         0.0    18.10               0 0.6930       5.887          94.7
205         0.0     2.46               0 0.4880       5.604          89.8
206        21.0     5.64               0 0.4390       6.511          21.1
207         0.0     2.89               0 0.4450       6.625          57.8
208         0.0     8.56               0 0.5200       5.851          96.7
209        55.0     3.78               0 0.4840       6.696          56.4
210         0.0     6.20               0 0.5040       5.981          68.1
211         0.0     6.20               1 0.5070       6.164          91.3
212         0.0     8.14               0 0.5380       6.072         100.0
213         0.0    27.74               0 0.6090       5.983          98.8
214         0.0    18.10               0 0.5840       6.348          86.1
215        12.5     7.87               0 0.5240       6.009          82.9
216        40.0     1.25               0 0.4290       6.490          44.4
217        34.0     6.09               0 0.4330       6.495          18.4
218         0.0     7.38               0 0.4930       6.312          28.9
219         0.0    19.58               1 0.8710       5.012          88.0
220         0.0    21.89               0 0.6240       5.857          98.2
221         0.0    18.10               0 0.6790       6.380          95.6
222        40.0     6.41               0 0.4470       6.482          32.1
223         0.0    18.10               0 0.6550       6.209          65.4
224         0.0    18.10               0 0.6550       5.759          48.2
225         0.0     2.89               0 0.4450       8.069          76.0
226        17.5     1.38               0 0.4161       7.104          59.5
227         0.0    18.10               0 0.5320       6.750          74.9
228         0.0    18.10               0 0.5320       5.762          40.3
229        20.0     3.97               0 0.5750       7.470          52.6
230         0.0    18.10               0 0.5970       5.757         100.0
231         0.0    18.10               0 0.5320       6.242          64.7
232         0.0    19.58               0 0.8710       5.628         100.0
233         0.0    18.10               0 0.7400       6.459          94.8
234        95.0     2.68               0 0.4161       7.853          33.2
235         0.0    19.58               0 0.6050       6.402          95.2
236         0.0     3.24               0 0.4600       5.868          25.8
237        25.0     5.13               0 0.4530       5.966          93.4
238         0.0     6.91               0 0.4480       5.786          33.3
239         0.0    18.10               0 0.7130       5.936          80.3
240         0.0     4.05               0 0.5100       6.416          84.1
241        22.0     5.86               0 0.4310       5.605          70.2
242         0.0    18.10               0 0.5830       5.905          53.2
243        20.0     6.96               1 0.4640       5.920          61.5
244         0.0     2.46               0 0.4880       7.765          83.3
245         0.0     5.96               0 0.4990       5.933          68.2
246         0.0     6.20               1 0.5070       6.951          88.5
247         0.0    10.01               0 0.5470       6.254          84.2
248         0.0     5.19               0 0.5150       5.895          59.6
249         0.0     6.91               0 0.4480       6.169           6.6
250         0.0     8.14               0 0.5380       6.047          88.8
251         0.0    18.10               0 0.6710       6.223         100.0
252        45.0     3.44               0 0.4370       7.185          38.9
253         0.0    18.10               0 0.7130       6.081          84.4
254        21.0     5.64               0 0.4390       6.115          63.0
255         0.0    18.10               0 0.7130       6.208          95.0
256         0.0     8.14               0 0.5380       6.674          87.3
257         0.0     4.05               0 0.5100       6.860          74.4
258         0.0    18.10               0 0.6930       6.405          96.0
259        20.0     3.97               0 0.6470       7.203          81.8
260        20.0     3.97               0 0.6470       7.327          94.5
261        22.0     5.86               0 0.4310       6.487          13.0
262         0.0    18.10               0 0.6710       7.313          97.9
263        80.0     3.64               0 0.3920       6.108          32.0
264         0.0    10.81               0 0.4130       6.065           7.8
265         0.0    10.01               0 0.5470       5.928          88.2
266         0.0    18.10               0 0.6930       4.519         100.0
267        25.0     5.13               0 0.4530       5.741          66.2
268         0.0    18.10               0 0.7000       5.536         100.0
269         0.0    18.10               0 0.5830       6.312          51.9
270        12.5     7.87               0 0.5240       6.004          85.9
271         0.0    18.10               0 0.7400       6.461          93.3
272         0.0     3.24               0 0.4600       6.333          17.2
273         0.0    12.83               0 0.4370       6.279          74.5
274         0.0    18.10               0 0.7000       4.652         100.0
275        40.0     1.25               0 0.4290       6.939          34.5
276         0.0    18.10               0 0.5830       6.114          79.8
277         0.0    18.10               0 0.5970       5.155         100.0
278        70.0     2.24               0 0.4000       7.041          10.0
279        45.0     3.44               0 0.4370       7.178          26.3
280         0.0     9.69               0 0.5850       5.794          70.6
281         0.0    18.10               0 0.7400       6.341          96.4
282         0.0    18.10               0 0.6790       6.782          90.8
283         0.0    18.10               0 0.7130       6.185          98.7
284        30.0     4.93               0 0.4280       6.393           7.8
285         0.0     4.49               0 0.4490       6.630          56.1
286        80.0     4.95               0 0.4110       6.630          23.4
287         0.0    18.10               0 0.5840       5.427          95.4
288        25.0     4.86               0 0.4260       6.302          32.2
289         0.0    18.10               0 0.5800       5.713          56.7
290         0.0    19.58               0 0.6050       5.877          79.2
291        34.0     6.09               0 0.4330       6.982          17.7
292         0.0    18.10               0 0.7000       5.713          97.0
293         0.0    12.83               0 0.4370       6.232          53.7
294         0.0    25.65               0 0.5810       5.986          88.4
295         0.0     9.69               0 0.5850       6.019          65.3
296        75.0     4.00               0 0.4100       5.888          47.6
297         0.0     6.91               0 0.4480       5.682          33.8
298         0.0    18.10               0 0.7400       6.219         100.0
299         0.0     8.56               0 0.5200       5.836          91.9
300        95.0     1.47               0 0.4030       6.975          15.3
301         0.0    25.65               0 0.5810       5.961          92.9
302         0.0     9.69               0 0.5850       5.926          42.6
303        60.0     2.93               0 0.4010       6.800           9.9
304         0.0     8.56               0 0.5200       6.167          90.0
305         0.0    18.10               0 0.5840       5.565          70.6
306         0.0    18.10               0 0.6680       4.906         100.0
307         0.0    10.01               0 0.5470       5.913          92.9
308         0.0    18.10               0 0.7130       6.513          89.9
309        52.5     5.32               0 0.4050       6.565          22.9
310         0.0    21.89               0 0.6240       5.693          96.0
311         0.0    19.58               0 0.6050       5.880          97.3
312        80.0     3.37               0 0.3980       5.787          31.1
313         0.0     4.05               0 0.5100       6.315          73.4
314         0.0     9.90               0 0.5440       6.382          67.2
315         0.0     9.90               0 0.5440       6.567          87.3
316         0.0     6.91               0 0.4480       6.211           6.5
317         0.0     5.19               0 0.5150       5.869          46.3
318         0.0    27.74               0 0.6090       5.093          98.0
319         0.0     9.90               0 0.5440       6.266          82.8
320         0.0    27.74               0 0.6090       5.983          83.5
321         0.0     4.05               0 0.5100       5.859          68.7
322         0.0     8.14               0 0.5380       5.456          36.6
323         0.0    13.92               0 0.4370       5.790          58.0
324        85.0     0.74               0 0.4100       6.383          35.7
325        52.5     5.32               0 0.4050       6.209          31.3
326         0.0    18.10               0 0.5840       5.837          59.7
327         0.0    18.10               0 0.7180       6.824          76.5
328        40.0     6.41               1 0.4470       6.826          27.6
329        60.0     2.93               0 0.4010       6.604          18.8
330         0.0    18.10               0 0.6710       6.794          98.8
331         0.0     1.89               0 0.5180       6.540          59.7
332        33.0     2.18               0 0.4720       6.849          70.3
333         0.0    18.10               0 0.6930       5.747          98.9
334         0.0    10.01               0 0.5470       5.731          65.2
335         0.0    18.10               0 0.6930       6.471          98.8
336         0.0    21.89               0 0.6240       6.458          98.9
337        22.0     5.86               0 0.4310       5.593          76.5
338         0.0    18.10               0 0.6790       6.202          78.7
339         0.0     2.18               0 0.4580       7.147          54.2
340         0.0    25.65               0 0.5810       5.879          95.8
341         0.0     6.20               1 0.5070       6.631          76.5
342        20.0     3.97               0 0.6470       7.206          91.6
343         0.0     4.49               0 0.4490       6.389          48.0
344         0.0    19.58               0 0.6050       5.854          91.8
345         0.0    13.89               1 0.5500       5.888          56.0
346         0.0    18.10               0 0.7400       6.251          96.6
347         0.0     9.90               0 0.5440       6.122          52.8
348         0.0    18.10               0 0.6930       5.987         100.0
349        90.0     1.22               0 0.4030       7.249          21.9
350         0.0    18.10               0 0.6140       6.103          85.1
351        45.0     3.44               0 0.4370       6.556          29.1
352         0.0     2.18               0 0.4580       6.430          58.7
353         0.0     8.56               0 0.5200       6.137          87.4
354         0.0    18.10               0 0.7000       6.051          82.5
355         0.0    19.58               0 0.8710       5.597          94.9
356         0.0     6.20               0 0.5070       6.086          61.5
357         0.0     8.14               0 0.5380       5.701          95.0
358        12.5     7.87               0 0.5240       6.012          66.6
359         0.0    25.65               0 0.5810       5.613          95.6
360         0.0     6.91               0 0.4480       6.069          40.0
361        20.0     3.97               0 0.6470       7.014          84.6
362         0.0    10.59               0 0.4890       5.783          72.7
363         0.0     2.46               0 0.4880       7.155          92.2
364        55.0     2.25               0 0.3890       6.453          31.9
365        20.0     3.97               0 0.6470       7.333         100.0
366         0.0     2.89               0 0.4450       7.820          36.9
367        82.5     2.03               0 0.4150       6.162          38.4
368         0.0     8.14               0 0.5380       5.935          29.3
369        80.0     3.37               0 0.3980       6.290          17.8
370         0.0     5.96               0 0.4990       5.841          61.4
371         0.0    18.10               0 0.7130       6.376          88.4
372        90.0     2.97               0 0.4000       7.088          20.8
373        12.5     7.87               0 0.5240       6.377          94.3
374        75.0     2.95               0 0.4280       7.024          15.8
375        20.0     3.33               1 0.4429       7.645          49.7
376         0.0    18.10               0 0.7700       5.362          96.2
377         0.0     6.20               0 0.5040       8.266          78.3
378        20.0     3.97               0 0.6470       5.560          62.8
379         0.0    18.10               1 0.7700       6.212          97.4
380        22.0     5.86               0 0.4310       6.226          79.2
381         0.0    25.65               0 0.5810       5.870          69.7
382         0.0    18.10               0 0.7400       5.854          96.6
383        22.0     5.86               0 0.4310       8.259           8.4
384         0.0    18.10               0 0.6930       5.683         100.0
385         0.0     4.05               0 0.5100       6.546          33.1
386         0.0     9.90               0 0.5440       5.914          83.2
387        30.0     4.93               0 0.4280       6.606          42.2
388        22.0     5.86               0 0.4310       6.438           8.9
389         0.0     9.69               0 0.5850       5.390          72.9
390        22.0     5.86               0 0.4310       6.108          34.9
391         0.0     8.14               0 0.5380       5.834          56.5
392         0.0     8.14               0 0.5380       5.570          98.1
393        35.0     6.06               0 0.4379       5.706          28.4
394         0.0    18.10               0 0.7130       6.317          83.0
395         0.0    18.10               0 0.7000       5.390          98.9
396        45.0     3.44               0 0.4370       6.782          41.1
397         0.0    10.59               0 0.4890       5.891          22.3
398         0.0     3.41               0 0.4890       6.417          66.1
399         0.0    10.01               0 0.5470       6.715          81.6
400         0.0    19.58               0 0.6050       6.101          93.0
401        80.0     1.52               0 0.4040       7.274          38.3
402         0.0    18.10               0 0.7400       6.485         100.0
403         0.0    19.58               1 0.6050       6.250          92.6
404         0.0     4.05               0 0.5100       5.572          88.5
405         0.0    19.58               0 0.8710       5.272          94.0
406         0.0     7.38               0 0.4930       6.415          40.1
407         0.0     7.38               0 0.4930       6.376          54.3
408         0.0     7.07               0 0.4690       7.185          61.1
409         0.0    18.10               0 0.5800       5.926          71.0
410         0.0     7.07               0 0.4690       6.421          78.9
411         0.0    18.10               0 0.6790       6.193          78.1
412         0.0    10.59               0 0.4890       5.412           9.8
413        20.0     6.96               1 0.4640       7.691          51.8
414        33.0     2.18               0 0.4720       6.616          58.1
415         0.0     8.14               0 0.5380       6.142          91.7
416        20.0     3.97               0 0.6470       7.520          89.4
417         0.0    18.10               0 0.7180       4.963          91.4
418         0.0     4.49               0 0.4490       6.015          45.1
419         0.0    18.10               0 0.5830       5.871          41.9
420         0.0    18.10               0 0.5970       4.628         100.0
421         0.0     8.56               0 0.5200       6.127          85.2
422         0.0    18.10               0 0.6680       4.138         100.0
423         0.0    10.59               1 0.4890       5.404          88.6
424         0.0     9.69               0 0.5850       5.569          73.5
425         0.0    12.83               0 0.4370       6.273           6.0
426         0.0     4.39               0 0.4420       5.898          52.3
427         0.0    21.89               0 0.6240       5.637          94.7
428         0.0    18.10               0 0.6310       3.863         100.0
429         0.0    21.89               0 0.6240       6.174          93.6
430         0.0    13.89               1 0.5500       5.951          93.8
431         0.0    18.10               0 0.6790       5.304          89.1
432         0.0    10.59               1 0.4890       5.344         100.0
433         0.0     8.14               0 0.5380       6.495          94.4
434        70.0     2.24               0 0.4000       6.871          47.4
435         0.0    18.10               0 0.5320       7.061          77.0
436        40.0     6.41               1 0.4470       6.758          32.9
437        45.0     3.44               0 0.4370       6.951          21.5
438         0.0     6.20               0 0.5040       6.552          21.4
439         0.0    19.58               0 0.8710       6.130         100.0
440        33.0     2.18               0 0.4720       7.420          71.9
441        35.0     1.52               0 0.4420       7.241          49.3
442         0.0    21.89               0 0.6240       6.151          97.9
443         0.0    21.89               0 0.6240       6.335          98.2
444         0.0    12.83               0 0.4370       6.140          45.8
445         0.0     2.89               0 0.4450       6.163          69.6
446         0.0     6.20               0 0.5070       8.247          70.4
447         0.0    18.10               0 0.7130       5.976          87.9
448         0.0     9.90               0 0.5440       4.973          37.8
449         0.0     7.38               0 0.4930       6.426          52.3
450         0.0     8.56               0 0.5200       6.195          54.4
451        18.0     2.31               0 0.5380       6.575          65.2
452         0.0    18.10               0 0.7130       6.297          91.8
453         0.0     5.19               0 0.5150       6.059          37.3
454         0.0     8.56               0 0.5200       6.405          85.4
455         0.0     5.19               0 0.5150       6.037          34.5
456        20.0     3.33               0 0.4429       6.968          37.2
457         0.0    21.89               0 0.6240       6.454          98.4
458         0.0     7.38               0 0.4930       6.041          49.9
459         0.0    12.83               0 0.4370       6.286          45.0
460         0.0    18.10               0 0.7000       5.000          89.5
461         0.0     5.96               0 0.4990       5.850          41.5
462        25.0     4.86               0 0.4260       6.167          46.7
463        25.0     4.86               0 0.4260       6.619          70.4
464        30.0     4.93               0 0.4280       6.358          52.9
465        20.0     6.96               0 0.4640       5.856          42.1
466         0.0    18.10               0 0.5970       5.617          97.9
467         0.0    18.10               0 0.7000       5.277          98.1
468         0.0     7.38               0 0.4930       6.431          14.7
469         0.0    25.65               0 0.5810       6.004          84.1
470         0.0     6.20               0 0.5040       7.686          17.0
471        80.0     3.64               0 0.3920       5.876          19.1
472         0.0    18.10               0 0.7400       6.629          94.6
473        85.0     4.15               0 0.4290       6.516          27.7
474         0.0     6.20               1 0.5070       6.879          77.7
475        25.0     4.86               0 0.4260       6.727          33.5
476         0.0    19.58               0 0.6050       6.319          96.1
477         0.0     2.46               0 0.4880       6.563          95.6
478         0.0    11.93               0 0.5730       6.976          91.0
479         0.0    10.59               1 0.4890       6.064          59.1
480        21.0     5.64               0 0.4390       5.998          21.4
    employ_dist radial_access tax_rate pupil_teacher_ratio lower_stat_pct
1        1.9669             4      437                21.2          16.90
2        4.8122             5      224                20.2           9.29
3        1.5331            24      666                20.2          24.56
4        2.2060            24      666                20.2          24.10
5        2.4961            24      666                20.2          18.71
6        5.2873             4      305                19.2           9.88
7        2.4527            24      666                20.2          16.74
8        1.8206            24      666                20.2          34.02
9        3.4211             5      276                16.4           9.69
10      10.5857             4      334                22.0           8.05
11       4.6947             5      216                14.9           3.76
12       1.3216             5      403                14.7          26.82
13       2.0651            24      666                20.2          19.52
14       3.0334            24      666                20.2          16.29
15       2.3889             1      273                21.0           6.48
16       2.3158            24      666                20.2          16.22
17       4.0952             4      307                21.0          19.88
18       5.4509             5      311                15.2          15.71
19       2.2955            24      666                20.2          14.19
20       1.2852            24      666                20.2          12.13
21       2.5451             5      384                20.9          15.55
22       3.9175             3      223                18.6           7.73
23       6.1899             6      300                16.6           6.36
24       1.7494             5      403                14.7          15.12
25      10.7103             4      411                18.3           7.79
26       8.3440             4      280                17.0           5.99
27       5.9604             4      289                16.0           6.27
28       1.9512            24      666                20.2          13.11
29       1.7700            24      666                20.2          25.68
30       3.0921             2      270                17.8           8.20
31       6.0877             3      233                17.9          16.20
32       1.4165            24      666                20.2          17.21
33       1.6232             5      403                14.7          15.79
34       2.7778             5      384                20.9           9.42
35       1.7912            24      666                20.2          15.17
36       3.9900             4      307                21.0          27.71
37       2.3460             4      437                21.2          17.31
38       2.5329            24      666                20.2          11.66
39       2.1850            24      666                20.2          19.31
40       1.8773             5      403                14.7           4.59
41       6.4584             5      224                20.2           6.75
42       3.6659             4      270                18.2           8.16
43       2.5480             6      432                17.8          17.09
44       3.7476             3      247                18.5           8.44
45       4.0317             4      304                18.4          15.94
46       3.2797             3      193                17.8          13.15
47       2.7831            24      666                20.2          16.23
48       7.8265             7      330                19.1           6.56
49       7.8278             5      358                14.8           4.97
50       4.7872             4      254                17.6           6.05
51       8.0136             3      352                18.8          10.53
52       2.2004            24      666                20.2          12.03
53       2.3817             6      391                19.2          12.01
54       2.3053            24      666                20.2          18.68
55       2.5052            24      666                20.2          13.27
56       5.7209             3      233                17.9           4.84
57       6.4654             5      370                17.6           4.61
58       1.8209             4      711                20.1          18.06
59       2.4786             1      273                21.0           9.67
60       1.3449            24      666                20.2          23.24
61       3.2721             8      307                17.4           7.60
62       4.3549             4      277                18.6          10.97
63       1.4118             5      403                14.7          26.42
64       1.5895            24      666                20.2          30.62
65       4.4546             4      307                21.0          16.51
66      10.5857             4      334                22.0           5.57
67       3.9454             4      277                18.6           9.47
68       5.6894             3      233                17.9          18.80
69       1.6180             5      403                14.7          14.10
70       4.4619             4      307                21.0          10.26
71       1.5192            24      666                20.2          21.08
72       1.7554             4      711                20.1          23.97
73       5.4159             5      287                19.6          12.79
74       2.2710             4      437                21.2          12.26
75       3.6519             8      307                17.4           8.05
76       4.1007             5      216                14.9           4.85
77       3.7598             4      307                21.0          20.34
78       4.2673             4      254                17.6           2.98
79       5.2873             4      305                19.2           7.54
80       8.3248             5      256                15.1           3.95
81       2.4259             5      403                14.7          14.43
82       1.8347            24      666                20.2          29.05
83       2.7986             6      391                19.2          17.60
84       4.2330             4      307                21.0          22.60
85       1.4655            24      666                20.2          19.78
86       2.8965            24      666                20.2          14.36
87       1.8589            24      666                20.2          15.02
88       2.4329             5      384                20.9          12.27
89       3.8473             5      279                19.2          10.13
90       2.7474             6      432                17.8          10.30
91       3.4217             2      270                17.8           5.50
92       4.2579             4      307                21.0          14.67
93       1.6390            24      666                20.2          20.31
94       2.3236            24      666                20.2          17.44
95       1.8746            24      666                20.2          15.70
96       2.2885             5      264                13.0           5.91
97       7.3090             2      329                12.6           8.61
98       6.3361             3      244                15.9           3.11
99       2.4358            24      666                20.2          18.13
100      3.4145             2      270                17.8           5.70
101      6.3361             6      300                16.6          12.40
102      2.5403            24      666                20.2          21.32
103      2.7227            24      666                20.2          11.48
104      2.1007            24      666                20.2          24.91
105      2.0107             5      264                13.0           6.90
106      1.5275            24      666                20.2          21.22
107      6.0622             3      222                18.7           2.94
108      7.2255             8      284                19.7           6.73
109      3.7965             4      307                21.0          11.28
110      1.4896            24      666                20.2          30.59
111      2.5091            24      666                20.2          12.67
112      1.6132            24      666                20.2           7.12
113     12.1265             5      187                17.0           4.50
114      3.6715             8      307                17.4           5.25
115      7.8265             7      330                19.1           9.52
116      2.8290             3      193                17.8           5.04
117      3.6659             4      270                18.2           6.21
118      1.4608             5      403                14.7          29.53
119      2.5975            24      666                20.2          16.42
120      4.7211             5      287                19.6          11.74
121      2.0882            24      666                20.2          19.69
122      4.6820             4      307                21.0          14.81
123      4.5026             5      398                18.7           9.10
124      2.5050             1      273                21.0           7.88
125      3.9454             4      277                18.6           9.38
126      3.3175             4      304                18.4           4.54
127      2.4775             6      432                17.8          15.37
128      2.4982             6      391                19.2          14.33
129      2.5182            24      666                20.2           7.79
130      4.3996             4      307                21.0          16.30
131      3.4952             2      276                18.0           6.19
132      7.8148             8      284                19.7           6.86
133      2.8340             4      304                18.4          11.72
134      6.8147             4      243                16.8          13.45
135      7.3172             6      293                16.6           7.60
136      1.1781            24      666                20.2          23.34
137      1.9047            24      666                20.2          14.64
138      4.4290             3      223                18.6           6.59
139      5.4011             3      252                18.3           4.32
140      1.9047            24      666                20.2           5.29
141      3.8771             4      277                18.6          17.27
142      1.7659             5      403                14.7           7.39
143      6.4980             4      345                18.9           8.10
144      5.1167             4      245                19.2           3.33
145      2.7301             6      432                17.8          12.04
146      2.2875             1      273                21.0           9.08
147      3.5549             5      296                16.6          10.11
148      1.9142            24      666                20.2          26.45
149      1.3459             5      403                14.7          29.29
150      3.1025             4      304                18.4           9.97
151      5.1167             4      245                19.2           3.56
152      1.8125             4      437                21.2          15.39
153      2.3552            24      666                20.2          17.73
154      1.4394             4      437                21.2          34.41
155      1.9444             2      188                19.1          25.41
156      1.8026            24      666                20.2          20.62
157      2.8561             5      384                20.9           7.67
158      8.9067             7      330                19.1           3.53
159      6.6407             1      304                16.9           7.83
160      2.1705            24      666                20.2          18.03
161      3.9450             4      304                18.4          11.50
162      5.5027             4      289                16.0          10.40
163      5.8700             3      233                17.9          30.81
164      1.5741            24      666                20.2          20.32
165      1.7455             5      403                14.7          15.02
166      2.8715            24      666                20.2          17.15
167      4.1480             8      307                17.4           4.73
168      1.8662            24      666                20.2          22.11
169      5.5027             4      289                16.0           8.58
170      6.9320             8      284                19.7           9.22
171      3.6526             4      277                18.6          16.03
172      3.2157             8      307                17.4           3.13
173      7.9809             8      284                19.7           9.50
174      1.3861            24      666                20.2          23.69
175      2.3274             4      437                21.2          11.12
176      2.5979             3      193                17.8           9.45
177     10.7103             4      411                18.3           5.49
178      4.7075             4      307                21.0           8.26
179      6.4980             4      345                18.9          13.09
180      6.4980             4      345                18.9           8.79
181      3.0993            24      666                20.2          12.87
182      3.6150             4      270                18.2          10.59
183      1.5296             5      403                14.7          28.32
184      7.6534             3      402                17.0           4.45
185      1.9512            24      666                20.2          14.10
186      5.9505             5      311                15.2          19.15
187      3.2157             8      307                17.4           6.36
188      5.9604             4      289                16.0           7.39
189      3.3633             5      276                16.4          10.50
190      4.8122             5      224                20.2           9.74
191      1.6074            24      666                20.2          27.38
192      4.0123             4      307                21.0          13.83
193      1.7573             5      403                14.7           6.43
194      1.8172            24      666                20.2          22.88
195      5.4917             7      329                16.1           9.50
196      1.5916             5      403                14.7          13.28
197      5.2873             4      305                19.2           6.72
198      1.4395            24      666                20.2          30.63
199      7.3090             2      329                12.6           4.08
200      2.4699             4      437                21.2          15.03
201      1.9096            24      666                20.2          24.39
202      1.5004            24      666                20.2          29.97
203      3.8384             8      307                17.4           2.47
204      1.7821            24      666                20.2          16.35
205      2.9879             3      193                17.8          13.98
206      6.8147             4      243                16.8           5.28
207      3.4952             2      276                18.0           6.65
208      2.1069             5      384                20.9          16.47
209      5.7321             5      370                17.6           7.18
210      3.6715             8      307                17.4          11.65
211      3.0480             8      307                17.4          21.46
212      4.1750             4      307                21.0          13.04
213      1.8681             4      711                20.1          18.07
214      2.0527            24      666                20.2          17.64
215      6.2267             5      311                15.2          13.27
216      8.7921             1      335                19.7           5.98
217      5.4917             7      329                16.1           8.67
218      5.4159             5      287                19.6           6.15
219      1.6102             5      403                14.7          12.12
220      1.6686             4      437                21.2          21.32
221      1.9682            24      666                20.2          24.08
222      4.1403             4      254                17.6           7.19
223      2.9634            24      666                20.2          13.22
224      3.0665            24      666                20.2          14.13
225      3.4952             2      276                18.0           4.21
226      9.2229             3      216                18.6           8.05
227      3.3317            24      666                20.2           7.74
228      4.0983            24      666                20.2          10.42
229      2.8720             5      264                13.0           3.16
230      1.4130            24      666                20.2          10.11
231      3.4242            24      666                20.2          10.74
232      1.5166             5      403                14.7          16.65
233      1.9879            24      666                20.2          23.98
234      5.1180             4      224                14.7           3.81
235      2.2625             5      403                14.7          11.32
236      5.2146             4      430                16.9           9.97
237      6.8185             8      284                19.7          14.44
238      5.1004             3      233                17.9          14.15
239      2.7792            24      666                20.2          16.94
240      2.6463             5      296                16.6           9.04
241      7.9549             7      330                19.1          18.46
242      3.1523            24      666                20.2          11.45
243      3.9175             3      223                18.6          13.65
244      2.7410             3      193                17.8           7.56
245      3.3603             5      279                19.2           9.68
246      2.8617             8      307                17.4           9.71
247      2.2565             6      432                17.8          10.45
248      5.6150             5      224                20.2          10.56
249      5.7209             3      233                17.9           5.81
250      4.4534             4      307                21.0          17.28
251      1.3861            24      666                20.2          21.78
252      4.5667             5      398                15.2           5.39
253      2.7175            24      666                20.2          14.70
254      6.8147             4      243                16.8           9.43
255      2.2222            24      666                20.2          15.17
256      4.2390             4      307                21.0          11.98
257      2.9153             5      296                16.6           6.92
258      1.6768            24      666                20.2          19.37
259      2.1121             5      264                13.0           9.59
260      2.0788             5      264                13.0          11.25
261      7.3967             7      330                19.1           5.90
262      1.3163            24      666                20.2          13.44
263      9.2203             1      315                16.4           6.57
264      5.2873             4      305                19.2           5.52
265      2.4631             6      432                17.8          15.76
266      1.6582            24      666                20.2          36.98
267      7.2254             8      284                19.7          13.15
268      1.5804            24      666                20.2          23.60
269      3.9917            24      666                20.2          10.58
270      6.5921             5      311                15.2          17.10
271      2.0026            24      666                20.2          18.05
272      5.2146             4      430                16.9           7.34
273      4.0522             5      398                18.7          11.97
274      1.4672            24      666                20.2          28.28
275      8.7921             1      335                19.7           5.89
276      3.5459            24      666                20.2          14.98
277      1.5894            24      666                20.2          20.08
278      7.8278             5      358                14.8           4.74
279      6.4798             5      398                15.2           2.87
280      2.8927             6      391                19.2          14.10
281      2.0720            24      666                20.2          17.79
282      1.8195            24      666                20.2          25.79
283      2.2616            24      666                20.2          18.13
284      7.0355             6      300                16.6           5.19
285      4.4377             3      247                18.5           6.53
286      5.1167             4      245                19.2           4.70
287      2.4298            24      666                20.2          18.14
288      5.4007             4      281                19.0           6.72
289      2.8237            24      666                20.2          14.76
290      2.4259             5      403                14.7          12.14
291      5.4917             7      329                16.1           4.86
292      1.9265            24      666                20.2          17.11
293      5.0141             5      398                18.7          12.34
294      1.9929             2      188                19.1          14.81
295      2.4091             6      391                19.2          12.92
296      7.3197             3      469                21.1          14.80
297      5.1004             3      233                17.9          10.21
298      2.0048            24      666                20.2          16.59
299      2.2110             5      384                20.9          18.66
300      7.6534             3      402                17.0           4.56
301      2.0869             2      188                19.1          17.93
302      2.3817             6      391                19.2          13.59
303      6.2196             1      265                15.6           5.03
304      2.4210             5      384                20.9          12.33
305      2.0635            24      666                20.2          17.16
306      1.1742            24      666                20.2          34.77
307      2.3534             6      432                17.8          16.21
308      2.8016            24      666                20.2          10.29
309      7.3172             6      293                16.6           9.51
310      1.7883             4      437                21.2          17.19
311      2.3887             5      403                14.7          12.03
312      6.6115             4      337                16.1          10.24
313      3.3175             5      296                16.6           6.29
314      3.5325             4      304                18.4          10.36
315      3.6023             4      304                18.4           9.28
316      5.7209             3      233                17.9           7.44
317      5.2311             5      224                20.2           9.80
318      1.8226             4      711                20.1          29.68
319      3.2628             4      304                18.4           7.90
320      2.1099             4      711                20.1          13.35
321      2.7019             5      296                16.6           9.64
322      3.7965             4      307                21.0          11.69
323      6.3200             4      289                16.0          15.84
324      9.1876             2      313                17.3           5.77
325      7.3172             6      293                16.6           7.14
326      1.9976            24      666                20.2          15.69
327      1.7940            24      666                20.2          22.74
328      4.8628             4      254                17.6           4.16
329      6.2196             1      265                15.6           4.38
330      1.3580            24      666                20.2          21.24
331      6.2669             1      422                15.9           8.65
332      3.1827             7      222                18.4           7.53
333      1.6334            24      666                20.2          19.92
334      2.7592             6      432                17.8          13.61
335      1.7257            24      666                20.2          17.12
336      2.1185             4      437                21.2          12.60
337      7.9549             7      330                19.1          12.50
338      1.8629            24      666                20.2          14.52
339      6.0622             3      222                18.7           5.33
340      2.0063             2      188                19.1          17.58
341      4.1480             8      307                17.4           9.54
342      1.9301             5      264                13.0           8.10
343      4.7794             3      247                18.5           9.62
344      2.4220             5      403                14.7          11.64
345      3.1121             5      276                16.4          13.51
346      2.1980            24      666                20.2          16.44
347      2.6403             4      304                18.4           5.98
348      1.5888            24      666                20.2          26.77
349      8.6966             5      226                17.9           4.81
350      2.0218            24      666                20.2          23.29
351      4.5667             5      398                15.2           4.56
352      6.0622             3      222                18.7           5.21
353      2.7147             5      384                20.9          13.44
354      2.1678            24      666                20.2          18.76
355      1.5257             5      403                14.7          21.45
356      3.6519             8      307                17.4          10.88
357      3.7872             4      307                21.0          18.35
358      5.5605             5      311                15.2          12.43
359      1.7572             2      188                19.1          27.26
360      5.7209             3      233                17.9           9.55
361      2.1329             5      264                13.0          14.79
362      4.3549             4      277                18.6          18.06
363      2.7006             3      193                17.8           4.82
364      7.3073             1      300                15.3           8.23
365      1.8946             5      264                13.0           7.79
366      3.4952             2      276                18.0           3.57
367      6.2700             2      348                14.7           7.43
368      4.4986             4      307                21.0           6.58
369      6.6115             4      337                16.1           4.67
370      3.3779             5      279                19.2          11.41
371      2.5671            24      666                20.2          14.65
372      7.3073             1      285                15.3           7.85
373      6.3467             5      311                15.2          20.45
374      5.4011             3      252                18.3           1.98
375      5.2119             5      216                14.9           3.01
376      2.1036            24      666                20.2          10.19
377      2.8944             8      307                17.4           4.14
378      1.9865             5      264                13.0          10.45
379      2.1222            24      666                20.2          17.60
380      8.0555             7      330                19.1          10.15
381      2.2577             2      188                19.1          14.37
382      1.8956            24      666                20.2          23.79
383      8.9067             7      330                19.1           3.54
384      1.4254            24      666                20.2          22.98
385      3.1323             5      296                16.6           5.33
386      3.9986             4      304                18.4          18.33
387      6.1899             6      300                16.6           7.37
388      7.3967             7      330                19.1           3.59
389      2.7986             6      391                19.2          21.14
390      8.0555             7      330                19.1           9.16
391      4.4986             4      307                21.0           8.47
392      3.7979             4      307                21.0          21.02
393      6.6407             1      304                16.9          12.43
394      2.7344            24      666                20.2          13.99
395      1.7281            24      666                20.2          20.85
396      3.7886             5      398                15.2           6.68
397      3.9454             4      277                18.6          10.87
398      3.0923             2      270                17.8           8.81
399      2.6775             6      432                17.8          10.16
400      2.2834             5      403                14.7           9.81
401      7.3090             2      329                12.6           6.62
402      1.9784            24      666                20.2          18.85
403      1.7984             5      403                14.7           5.50
404      2.5961             5      296                16.6          14.69
405      1.7364             5      403                14.7          16.14
406      4.7211             5      287                19.6           6.12
407      4.5404             5      287                19.6           6.87
408      4.9671             2      242                17.8           4.03
409      2.9084            24      666                20.2          18.13
410      4.9671             2      242                17.8           9.14
411      1.9356            24      666                20.2          21.52
412      3.5875             4      277                18.6          29.55
413      4.3665             3      223                18.6           6.58
414      3.3700             7      222                18.4           8.93
415      3.9769             4      307                21.0          18.72
416      2.1398             5      264                13.0           7.26
417      1.7523            24      666                20.2          14.00
418      4.4272             3      247                18.5          12.86
419      3.7240            24      666                20.2          13.34
420      1.5539            24      666                20.2          34.37
421      2.1224             5      384                20.9          14.09
422      1.1370            24      666                20.2          37.97
423      3.6650             4      277                18.6          23.98
424      2.3999             6      391                19.2          15.10
425      4.2515             5      398                18.7           6.78
426      8.0136             3      352                18.8          12.67
427      1.9799             4      437                21.2          18.34
428      1.5106            24      666                20.2          13.33
429      1.6119             4      437                21.2          24.16
430      2.8893             5      276                16.4          17.92
431      1.6475            24      666                20.2          26.64
432      3.8750             4      277                18.6          23.09
433      4.4547             4      307                21.0          12.80
434      7.8278             5      358                14.8           6.07
435      3.4106            24      666                20.2           7.01
436      4.0776             4      254                17.6           3.53
437      6.4798             5      398                15.2           5.10
438      3.3751             8      307                17.4           3.76
439      1.4191             5      403                14.7          27.80
440      3.0992             7      222                18.4           6.47
441      7.0379             1      284                15.5           5.49
442      1.6687             4      437                21.2          18.46
443      2.1107             4      437                21.2          16.96
444      4.0905             5      398                18.7          10.27
445      3.4952             2      276                18.0          11.34
446      3.6519             8      307                17.4           3.95
447      2.5806            24      666                20.2          19.01
448      2.5194             4      304                18.4          12.64
449      4.5404             5      287                19.6           7.20
450      2.7778             5      384                20.9          13.00
451      4.0900             1      296                15.3           4.98
452      2.3682            24      666                20.2          17.27
453      4.8122             5      224                20.2           8.51
454      2.7147             5      384                20.9          10.63
455      5.9853             5      224                20.2           8.01
456      5.2447             5      216                14.9           4.59
457      1.8498             4      437                21.2          14.59
458      4.7211             5      287                19.6           7.70
459      4.5026             5      398                18.7           8.94
460      1.5184            24      666                20.2          31.99
461      3.9342             5      279                19.2           8.77
462      5.4007             4      281                19.0           7.51
463      5.4007             4      281                19.0           7.22
464      7.0355             6      300                16.6          11.22
465      4.4290             3      223                18.6          13.00
466      1.4547            24      666                20.2          26.40
467      1.4261            24      666                20.2          30.81
468      5.4159             5      287                19.6           5.08
469      2.1974             2      188                19.1          14.27
470      3.3751             8      307                17.4           3.92
471      9.2203             1      315                16.4           9.25
472      2.1247            24      666                20.2          23.27
473      8.5353             4      351                17.9           6.36
474      3.2721             8      307                17.4           9.93
475      5.4007             4      281                19.0           5.29
476      2.1000             5      403                14.7          11.10
477      2.8470             3      193                17.8           5.68
478      2.1675             1      273                21.0           5.64
479      4.2392             4      277                18.6          14.66
480      6.8147             4      243                16.8           8.43
    dist_fenway_park
1          5238.4649
2         16343.7994
3          9473.0404
4          7692.1031
5          8409.6621
6          2137.6604
7          8835.9189
8          8054.4195
9          4516.7075
10        29213.9834
11         9566.9624
12         7084.5010
13         9099.9205
14         6940.3943
15        12995.2441
16         7983.2537
17        14045.1213
18        16346.2229
19         5065.9960
20         7843.3768
21         5323.0309
22         7284.0197
23        13337.6577
24         5835.2694
25        33638.4011
26        21633.5409
27         9090.1756
28         6435.7633
29         9729.6859
30         6668.9243
31        16140.2464
32         7087.6383
33         5983.7672
34         4744.0380
35        10393.9951
36        14170.6464
37         4496.0298
38         6444.8955
39         8423.2204
40         5292.7403
41        17193.7943
42         5432.6896
43         6851.6991
44         6813.9032
45        12732.5156
46         4606.8190
47         8469.5523
48        17732.6484
49        10193.8505
50         8170.8771
51        19445.1093
52         7693.4523
53        10106.2800
54         7300.8939
55         4855.8948
56        10388.8084
57        20045.9642
58         9616.0707
59        13067.0246
60         8276.9901
61         5311.2581
62         7199.5418
63         6734.6795
64         9696.1657
65        15004.5347
66        29566.6615
67         5245.9610
68        15771.8495
69         5921.5950
70        14107.7472
71         7563.3942
72         9238.2523
73        12666.7534
74         4570.8177
75         6137.9940
76         8030.5325
77        13599.9112
78         7713.2559
79         3474.0827
80        18695.8489
81         4350.3472
82         7936.1757
83        10210.6082
84        14703.3965
85         7675.5408
86         6377.6435
87         6626.0895
88         5841.4786
89         8859.4273
90         8239.0673
91         6607.4227
92        13459.7352
93         9192.3094
94         8261.2299
95         6336.4263
96         5501.0021
97        16111.5536
98        15760.8220
99         7968.9193
100        7404.1003
101       14530.5958
102        7004.9787
103        4935.8109
104        7455.4726
105        5520.5627
106        7441.3568
107       18940.0623
108       19571.4132
109       12414.0013
110        9642.9388
111        5052.2148
112        6543.8707
113       31656.0945
114        6533.1389
115       18589.1409
116        3822.5389
117        4326.1532
118        6459.4829
119        8706.4386
120       14756.0871
121        7734.2648
122       15462.4676
123        1649.4173
124       13555.9718
125        6004.6916
126       11572.6249
127        8293.6710
128       12355.3798
129        5218.1759
130       14435.3621
131        3420.6876
132       17671.9771
133       11220.3051
134       16286.7237
135        9906.7218
136        7935.6286
137        4890.9198
138        7617.2250
139        9456.3154
140        6516.7246
141        6929.6055
142        5742.0587
143         887.9007
144        9252.2245
145        7487.5091
146       12585.6906
147        3708.5164
148        8106.5137
149        6869.5930
150       10915.8069
151        8411.1472
152        5939.7786
153        8692.9900
154        6451.1144
155        7669.0097
156        7293.8084
157        4083.1474
158       19838.8447
159       14606.7235
160        7257.2983
161       14774.5334
162        8424.2491
163       15872.2869
164        9136.0534
165        5754.3366
166        7962.3354
167        7746.7201
168        9139.4539
169        8624.8190
170       17512.8200
171        5952.7918
172        5848.7851
173       21124.6041
174        7740.9521
175        4586.2048
176        4265.6108
177       31311.8977
178       14908.4883
179        1219.1524
180        1683.7868
181        6581.5293
182        4573.9695
183        6318.3127
184       18980.6047
185        6388.7543
186       17832.2322
187        5855.1010
188        9156.0464
189        4715.4110
190       16195.1959
191        8760.3656
192       13046.2223
193        5542.1011
194        8678.0120
195        9135.5190
196        5991.3141
197        2862.7360
198        9237.0239
199       13927.6780
200        4186.7061
201        6972.2592
202        8828.0972
203        7250.9033
204       10110.7373
205        4508.0908
206       15501.2481
207        3433.3156
208        5101.5766
209       19238.8280
210        6774.5257
211        5375.5246
212       15047.8081
213        9854.6118
214        7399.4823
215       17093.0247
216       30592.9190
217        9634.6127
218       13672.1089
219        6322.2493
220        5816.9151
221        7781.8443
222        7584.3011
223        8788.9281
224        8064.6388
225        2855.6581
226       26410.6025
227        6260.9940
228        6695.6112
229        5039.8596
230        7581.2102
231        6231.5406
232        6216.2745
233        8335.6144
234       12051.8258
235        4580.2701
236       11464.1463
237       18630.8459
238       14789.3535
239        8156.5825
240        3886.8531
241       19031.9496
242        7595.8202
243        6941.1962
244        4045.2572
245       11173.1712
246        4992.2983
247        7281.6420
248       17199.8000
249       10524.6468
250       15485.9714
251        7686.0208
252        6069.8522
253        8805.8037
254       14947.6319
255        8062.2839
256       16468.0031
257        3587.9753
258        9548.6701
259        5486.9077
260        5901.9554
261       16634.3068
262        8062.1112
263       22449.8060
264        3939.9613
265        7634.4679
266        8147.4289
267       18621.3382
268        9296.3644
269        7662.8123
270       18761.9700
271        8086.7301
272       10411.0769
273        2410.1839
274        9410.3095
275       28087.6861
276        7480.3086
277        7816.9277
278       10370.6334
279        4767.8149
280       11940.9719
281        8677.5186
282        7729.6003
283        8711.8125
284       16251.0737
285        5520.8964
286        7854.5197
287        7546.2759
288        3393.0937
289        7021.7540
290        4209.2310
291        8256.4009
292       10493.6501
293        2002.5327
294        8746.5086
295       10898.4570
296        8923.7167
297       13958.4593
298        9051.2783
299        5398.4562
300       16757.7086
301        7539.8803
302       10057.8554
303        6373.9386
304        4745.1510
305        7015.7237
306        8388.5783
307        6343.3426
308        9411.5763
309       11017.2644
310        6349.3144
311        4366.9466
312        3152.3162
313        3570.1469
314       12031.4858
315       12888.6235
316       13355.9132
317       15640.8449
318        9015.7568
319       12025.4885
320        8370.1403
321        3893.2824
322       11887.8725
323        9181.6403
324       18644.8783
325       11214.1275
326        7190.6333
327        6819.3281
328        8535.7841
329        7517.3084
330        7891.5023
331       21383.1730
332       10321.0481
333        9580.1005
334        9248.0261
335        9916.1187
336        4979.0162
337       17564.2345
338        7241.1912
339       19587.5651
340        8255.4436
341        7506.7589
342        5944.9225
343        6200.8293
344        4369.1618
345        4944.1547
346        8911.5802
347       11700.2876
348        8908.7407
349       15052.2791
350        6741.9622
351        5861.5894
352       20179.7201
353        4177.0965
354       11213.2652
355        6241.3712
356        6581.4851
357       13353.3583
358       18039.4036
359        8099.7890
360       14482.9883
361        6072.5372
362        7194.4639
363        4261.9265
364       15684.3670
365        5704.5868
366        2813.4930
367       14547.7925
368       12394.9368
369        5816.6830
370       10270.1090
371        9305.9577
372       12528.4756
373       18095.2412
374        7530.0840
375       10888.2425
376        5312.9113
377        5259.0329
378        6094.1946
379        4925.7356
380       17830.9959
381        8861.4477
382        8427.8481
383       21352.7781
384        8866.5031
385        3228.8684
386       14112.3139
387       13144.8176
388       17129.7775
389       11240.0788
390       19415.6071
391       13575.1346
392       12909.4077
393       13393.8772
394        9759.8588
395        9924.6558
396        4254.7987
397        6691.5642
398        7954.8444
399        6339.8857
400        4548.3673
401       14039.8979
402        8721.2027
403        5437.9799
404        3951.0116
405        5691.8703
406       14392.4764
407       13502.1315
408       18096.7701
409        7119.0384
410       16530.1637
411        7454.0070
412        5205.8784
413        7380.5340
414        8312.9514
415       13552.0341
416        5594.1433
417        7013.5593
418        7307.4067
419        7192.6924
420        7624.0807
421        5901.7874
422        8362.7801
423        6388.4373
424       11611.7816
425        2543.0284
426       18963.7459
427        5434.3751
428        7217.5147
429        6551.0858
430        4510.4554
431        7456.5456
432        6792.2107
433       15796.7687
434        9866.9153
435        6541.2136
436        7435.2752
437        3865.4572
438        6446.5728
439        6660.0582
440        8925.0890
441       24448.8585
442        6160.5469
443        4686.6483
444        3133.7288
445        2837.0093
446        6563.7117
447        8044.1832
448       10943.2247
449       12624.9018
450        5542.2478
451       16177.5143
452        9282.5164
453       16720.5551
454        3863.9409
455       16455.6330
456       11369.1309
457        5608.6548
458       14144.8881
459        2148.1446
460        9509.5254
461       10604.4329
462        4550.9748
463        3343.4777
464       14943.5273
465        7498.9021
466        7850.6513
467        9372.9214
468       13870.6762
469        8128.8589
470        5991.5091
471       20401.3624
472        8113.6098
473       21226.5956
474        5704.1426
475        3488.4907
476        4840.6591
477        4323.4338
478       12208.1097
479        7413.9896
480       13275.6229
suppressMessages(library(geosphere))
suppressMessages(library(leaflet))

1. Kriminalitet i Boston

I detta avsnitt ska ni analysera kriminaliteten i Boston med hjälp av variabeln crime_rate.

💪 Uppgift 1.1

Vad kan man generellt säga om kriminaliteten i Boston 1970? Använd lämpliga figurer och mått för att ge en beskrivning.

Uppgift 1.1 - Svar

Skriv svaret här. Vid behov skrivs matematiska symboler inom dollartecken, till exempel \(\overline{y} = \cfrac{\sum^{n}_{i=1} y_i}{n}\). Koden skrivs i R-rutan nedanför.

suppressMessages(library(mosaic))
favstats(~crime_rate, data = Boston_census)
     min        Q1   median       Q3     max    mean       sd   n missing
 0.00632 0.0829725 0.253715 3.681942 88.9762 3.66526 8.746156 480       0
bwplot(~crime_rate, data = Boston_census)

Crime_rate = Boston_census[,5]
Crime_rate
  [1]  0.32264  0.06151  7.99248  6.39312  9.51363  0.15876  8.24809 13.67810
  [9]  0.07013  0.04301  0.03578  3.32105  9.72418  4.34879  0.10959  5.58107
 [17]  0.98843  0.09378  3.83684 11.95110  0.26363  0.11460  0.08244  1.41385
 [25]  0.07244  0.01501  0.12932 14.33370 11.57790  0.03932  0.21977 88.97620
 [33]  2.14918  0.14866  8.64476  1.38799  0.97617  4.64689  7.52601  1.22358
 [41]  0.03738  0.04203  0.22212  0.07151  0.24522  0.06047  7.75223  0.19073
 [49]  0.06466  0.10469  0.03113  6.44405  0.17331  4.87141  3.84970  0.12744
 [57]  0.03049  0.15086  0.06263 15.28800  0.61470  0.22969  4.09740 14.33370
 [65]  0.84054  0.10659  0.19802  0.22927  1.65660  0.63796 15.87440  0.18337
 [73]  0.24103  1.19294  0.44791  0.21038  1.61282  0.09604  0.19539  0.01432
 [81]  1.20742 18.08460  0.17899  1.13081 14.43830  3.56868 11.08740  0.12802
 [89]  0.17505  0.15098  0.05660  0.78420  9.59571  6.71772  7.02259  0.52014
 [97]  0.04666  0.01538  4.75237  0.05302  0.10612  4.42228  5.20177 15.02340
[105]  0.65665 14.05070  0.03237  0.11027  0.72580 38.35180  4.26131  4.55587
[113]  0.01709  0.46296  0.16439  0.05780  0.02875  2.36862  4.81213  0.28392
[121] 10.06230  0.67191  0.08387  0.04741  0.14052  0.49298  0.13058  0.22438
[129]  4.54192  0.75026  0.06860  0.15445  0.26169  0.08873  0.04590 20.71620
[137]  4.22239  0.16211  0.02763  3.47428  0.17446  1.42502  0.05789  0.03502
[145]  0.13158  0.04527  0.07022 15.17720  2.77974  0.34940  0.07886  0.32543
[153]  5.44114  1.62864  0.15038 73.53410  0.11432  0.08221  0.03466 10.23300
[161]  0.25356  0.08199  0.25387 14.23620  3.53501  3.77498  0.51183 22.05110
[169]  0.08265  0.10328  0.21719  0.38214  0.12650 23.64820  0.59005  0.06888
[177]  0.07950  0.62976  0.13554  0.12816  4.03841  0.04294  2.33099  0.01778
[185] 12.04820  0.14455  0.41238  0.05372  0.11425  0.05497 41.52920  0.85204
[193]  1.34284  9.39063  0.03537  1.49632  0.08826 20.08490  0.04011  0.32982
[201] 15.86030  9.91655  0.57529 13.35980  0.08308  0.05360  0.12204  0.13262
[209]  0.02543  0.53700  0.40771  1.35472  0.10574  8.49213  0.11747  0.06211
[217]  0.09266  0.30347  1.12658  0.24980  9.33889  0.07978  7.83932  3.16360
[225]  0.12083  0.01951  5.70818  2.81838  0.54050 51.13580  5.82401  2.15505
[233] 10.67180  0.03510  2.44953  0.06617  0.17171  0.18836  8.20058  0.09178
[241]  0.19133  4.83567  0.09065  0.06588  0.06417  0.35809  0.14231  0.03041
[249]  0.14150  0.95577 17.86670  0.08370  6.80117  0.04337 13.91340  1.00245
[257]  0.06642  5.87205  0.54011  0.82526  0.14030 19.60910  0.04819  0.09164
[265]  0.17134 45.74610  0.14932  9.18702  3.67367  0.17004 14.42080  0.06724
[273]  0.10153 24.39380  0.02899  5.69175 28.65580  0.05561  0.08664  0.26838
[281]  6.28807 10.83420  9.32909  0.12757  0.05735  0.03615  8.05579  0.03659
[289] 13.07510  1.80028  0.10000  6.96215  0.05646  0.16902  0.23912  0.01360
[297]  0.17142  5.66637  0.17120  0.03150  0.09299  0.27957  0.02187  0.13960
[305]  8.79212 11.10810  0.12329  5.82115  0.04297  0.25915  2.31390  0.04379
[313]  0.05425  0.40202  0.36920  0.15936  0.03427  0.20746  0.26938  0.11132
[321]  0.08447  0.80271  0.14103  0.02055  0.03871 12.24720 11.81230  0.06127
[329]  0.01439  9.82349  0.02498  0.04932  7.67202  0.14476  8.71675  0.34006
[337]  0.20608 37.66190  0.06905  0.09849  0.52058  0.55007  0.05059  2.24236
[345]  0.04560  9.92485  0.79041 25.04610  0.01311  7.05042  0.12579  0.02985
[353]  0.21161  5.29305  2.73397  0.33045  1.15172  0.08829  0.38735  0.12269
[361]  0.78570  0.25199  0.09103  0.01096  0.66351  0.08187  0.03445  1.05393
[369]  0.03584  0.09744  3.69311  0.00906  0.22489  0.03359  0.06129  3.67822
[377]  0.31533  0.76162  8.98296  0.19657  0.06899 12.80230  0.36894 67.92080
[385]  0.06664  0.31827  0.09252  0.21409  0.28960  0.33983  0.62739  1.25179
[393]  0.05023  6.65492  8.15174  0.07875  0.13642  0.04684  0.10084  2.92400
[401]  0.03768  9.96654  1.27346  0.13914  2.44668  0.34109  0.18159  0.02729
[409] 15.57570  0.02731  7.36711  0.28955  0.22188  0.05479  1.23247  0.53412
[417]  3.69695  0.05188  2.37857 18.81100  0.13117 18.49820  0.37578  0.17783
[425]  0.07896  0.06162  0.88125 13.52220  0.29090  0.11069 25.94060  0.43571
[433]  0.77299  0.04417  5.73116  0.05644  0.09068  0.44178  2.37934  0.07503
[441]  0.01301  0.54452  0.55778  0.08707  0.11504  0.33147  4.66883  2.63548
[449]  0.16760  0.10793  0.00632  5.09017  0.03306  0.22876  0.03961  0.03705
[457]  0.35233  0.35114  0.09512 22.59710  0.08014  0.03551  0.04462  0.10290
[465]  0.29916  7.40389 16.81180  0.19186  0.07165  0.29819  0.03548 11.16040
[473]  0.01870  0.62356  0.04113  2.30040  0.10008  0.06076  0.13587  0.04981
log_crime_rate <- log(Crime_rate)
log_crime_rate
  [1] -1.131218128 -2.788555516  2.078501100  1.855222412  2.252725507
  [6] -1.840361651  2.109981658  2.615796014 -2.657404616 -3.146322632
 [11] -3.330366201  1.200280998  2.274615567  1.469897645 -2.211009150
 [16]  1.719380514 -0.011637453 -2.366803665  1.344649111  2.480823324
 [21] -1.333208674 -2.166307475 -2.495684523  0.346316480 -2.624996646
 [26] -4.199038633 -2.045465326  2.662613408  2.449098109 -3.236021984
 [31] -1.515173734  4.488368918  0.765086374 -1.906093460  2.156953357
 [36]  0.327856657 -0.024118527  1.536198179  2.018365021  0.201780988
 [41] -3.286619477 -3.169371630 -1.504537503 -2.637917979 -1.405599512
 [46] -2.805607905  2.047980544 -1.656896464 -2.738612507 -2.256751677
 [51] -3.469583295  1.863157224 -1.752673381  1.583383423  1.347995223
 [56] -2.060109613 -3.490356518 -1.891403025 -2.770510882  2.727068207
 [61] -0.486620935 -1.471024705  1.410352626  2.662613408 -0.173710737
 [66] -2.238765580 -1.619387243 -1.472854931  0.504767309 -0.449479694
 [71]  2.764707749 -1.696249309 -1.422833872  0.176420848 -0.803162960
 [76] -1.558839860  0.477984200 -2.342990508 -1.632757718 -4.246098117
 [81]  0.188485852  2.895060747 -1.720425341  0.122934190  2.669884398
 [86]  1.272195780  2.405809328 -2.055568777 -1.742683632 -1.890607901
 [91] -2.871746294 -0.243091189  2.261316124  1.904748811  1.949132096
 [96] -0.653657273 -3.064868012 -4.174687315  1.558643441 -2.937086078
[101] -2.243184750  1.486655400  1.648998952  2.709608986 -0.420604127
[106]  2.642672217 -3.430523211 -2.204823375 -0.320480784  3.646801463
[111]  1.449576625  1.516416511 -4.069261782 -0.770114622 -1.805513625
[116] -2.850766503 -3.549117512  0.862307507  1.571139814 -1.259062771
[121]  2.308795767 -0.397630876 -2.478487298 -3.048922102 -1.962405452
[126] -0.707286674 -2.035769213 -1.494414236  1.513349830 -0.287335466
[131] -2.679462744 -1.867884860 -1.340594682 -2.422157228 -3.081290162
[136]  3.030916003  1.440401318 -1.819480162 -3.588853140  1.245387263
[141] -1.746059790  0.354185849 -2.849210621 -3.351835952 -2.028140247
[146] -3.095110718 -2.656122108  2.719794302  1.022357398 -1.051537881
[151] -2.540081151 -1.122607894  1.693988598  0.487745311 -1.894589855
[156]  4.297749244 -2.168753745 -2.498478330 -3.362168995  2.325617792
[161] -1.372154798 -2.501157990 -1.370932954  2.655788016  1.262716128
[166]  1.328395085 -0.669762740  3.093362487 -2.493140455 -2.270311532
[171] -1.526982732 -0.961968245 -2.067512971  3.163287002 -0.527548000
[176] -2.675389419 -2.531998257 -0.462416485 -1.998488479 -2.054475796
[181]  1.395851050 -3.147951487  0.846293070 -4.029681049  2.488915271
[186] -1.934129811 -0.885810025 -2.923969907 -2.169366249 -2.900967697
[191]  3.726396794 -0.160121805  0.294786774  2.239712384 -3.341891276
[196]  0.403008760 -2.427468275  2.999968289 -3.216129599 -1.109208228
[201]  2.763819132  2.294205079 -0.552881017  2.592250198 -2.487951280
[206] -2.926206211 -2.103406419 -2.020267383 -3.671825700 -0.621757184
[211] -0.897199142  0.303594791 -2.246772028  2.139139852 -2.141572297
[216] -2.778848272 -2.378818399 -1.192472520  0.119186495 -1.387094681
[221]  2.234187401 -2.528482433  2.059152096  1.151710620 -2.113370680
[226] -3.936828124  1.741900234  1.036162252 -0.615260642  3.934484839
[231]  1.761989028  0.767813925  2.367604748 -3.349554149  0.895896169
[236] -2.715528091 -1.761948272 -1.669400254  2.104204883 -2.388360870
[241] -1.653755593  1.576019692 -2.400749342 -2.719920374 -2.746219467
[246] -1.026970928 -1.949747502 -3.492983777 -1.955455562 -0.045237981
[251]  2.882938645 -2.480516301  1.917094656 -3.137987321  2.632852405
[256]  0.002447004 -2.711757063  1.770203806 -0.615982456 -0.192056791
[261] -1.963972292  2.975993744 -3.032603748 -2.389887421 -1.764105392
[266]  3.823106542 -1.901663625  2.217791618  1.301191162 -1.771721575
[271]  2.668671609 -2.699486970 -2.287400958  3.194329002 -3.540804336
[276]  1.739017758  3.355355866 -2.889392238 -2.445993676 -1.315351392
[281]  1.838654187  2.382707797  2.233137475 -2.059090045 -2.858582435
[286] -3.320078330  2.086391088 -3.307980300  2.570709658  0.587942208
[291] -2.302585093  1.940488335 -2.874222856 -1.777738228 -1.430789761
[296] -4.297685486 -1.763638594  1.734548701 -1.764922815 -3.457767733
[301] -2.375263318 -1.274502571 -3.822639444 -1.968974089  2.173855866
[306]  2.407674572 -2.093215975  1.761497837 -3.147253081 -1.350348234
[311]  0.838934413 -3.128349798 -2.914152287 -0.911253440 -0.996416776
[316] -1.836589485 -3.373484943 -1.572816729 -1.311632257 -2.195346342
[321] -2.471358837 -0.219761776 -1.958782645 -3.884894338 -3.251657314
[326]  2.505297339  2.469141361 -2.792464952 -4.241221758  2.284776456
[331] -3.689679774 -3.009425601  2.037579944 -1.932678080  2.165246462
[336] -1.078633206 -1.579490836  3.628648973 -2.672924399 -2.317800259
[341] -0.652811704 -0.597709736 -2.984001351  0.807528883 -3.087847562
[346]  2.295041713 -0.235203481  3.220718127 -4.334379981  1.953087190
[351] -2.073141429 -3.511570439 -1.553010321  1.666394639  1.005754765
[356] -1.107299917  0.141256477 -2.427128428 -0.948426602 -2.098094430
[361] -0.241180239 -1.378365875 -2.396566156 -4.513502997 -0.410211354
[366] -2.502622656 -3.368246282  0.052526034 -3.328690691 -2.328518475
[371]  1.306468922 -4.703886159 -1.492143885 -3.393526875 -2.792138581
[376]  1.302428940 -1.154135569 -0.272307535  2.195329449 -1.626736677
[381] -2.673793712  2.549624842 -0.997121250  4.218342320 -2.708450281
[386] -1.144855200 -2.380330442 -1.541358792 -1.239254618 -1.079309786
[391] -0.466186922  0.224574527 -2.991142821  1.895356431  2.098231401
[396] -2.541477001 -1.992016917 -3.061017740 -2.294220177  1.072952542
[401] -3.278625829  2.299233483  0.241737605 -1.972274658  0.894732004
[406] -1.075608907 -1.706003880 -3.601234944  2.745712007 -3.600502343
[411]  1.997025499 -1.239427285 -1.505618584 -2.904247583  0.209020286
[416] -0.627134746  1.307508155 -2.958821920  0.866499467  2.934441805
[421] -2.031261087  2.917673430 -0.978751413 -1.726927241 -2.538813884
[426] -2.786768786 -0.126413925  2.604332779 -1.234775713 -2.201021778
[431]  3.255809309 -0.830778395 -0.257489167 -3.119709453  1.745917954
[436] -2.874577152 -2.400418453 -0.816943258  0.866823138 -2.589867245
[441] -4.342036986 -0.607850606 -0.583790660 -2.441042886 -2.162475385
[446] -1.104217971  1.540908505  0.969065329 -1.786175091 -2.226272410
[451] -5.064036071  1.627311229 -3.409431187 -1.475081860 -3.228673667
[456] -3.295486927 -1.043187043 -1.046570275 -2.352616027  3.117821579
[461] -2.523980174 -3.337940932 -3.109573090 -2.273997636 -1.206776732
[466]  2.002005538  2.822081021 -1.650989340 -2.635962125 -1.210024412
[471] -3.338786122  2.412371799 -3.979231755 -0.472310288 -3.191017497
[476]  0.833083021 -2.301785413 -2.800823601 -1.996056733 -2.999539512
bwplot(log_crime_rate) #transformerad plot

#svar: Vi kan säga att enligt beskrivningen ser vi att crime_rate variabeln har medelvärdet är ca 3.67 och histogram kan vi ta reda på en del outlier som påverkar vår medelvärdet. Generellt kan vi säga Boston 1970 har low kriminaliteten.

💪 Uppgift 1.2

Distrikten tillhör olika stadsdelar som anges i den kategoriska variabeln town? Det finns 88 olika sådana stadsdelar (towns).

Skiljer sig brottsligheten åt mellan de olika stadsdelarna? Undersök stadsdelarna Boston East Boston, Boston Downtown, Cambridge, samt ytterligare en stadsdel som ni själva väljer. Besvara frågan med hjälp av lämpligt valda figurer och statistiska mått.

Tip

Innan ni påbörjar analysen, skapa en ny data frame som enbart innehåller de stadsdelar som ni vill jämföra. Det kan göras till exempel med funktionen filter().

Uppgift 1.2 - Svar

Skriv svaret här.

suppressMessages(library(dplyr))
Boston_census_new <- filter(Boston_census, town == "Boston East Boston" |town == "Boston Downtown" |town == "Cambridge" | town == "Newton")
Boston_census_new
                 town longitude latitude median_home_value crime_rate
1  Boston East Boston  -71.0215  42.2270              12.3    7.99248
2           Cambridge  -71.0480  42.2222              13.4    3.32105
3     Boston Downtown  -71.0427  42.2090              27.9   11.95110
4           Cambridge  -71.0662  42.2162              17.0    1.41385
5  Boston East Boston  -71.0200  42.2205               9.7   11.57790
6           Cambridge  -71.0645  42.2150              19.4    2.14918
7           Cambridge  -71.0690  42.2285              41.3    1.22358
8              Newton  -71.1208  42.2183              30.1    0.61470
9           Cambridge  -71.0519  42.2230              15.6    4.09740
10 Boston East Boston  -71.0195  42.2255              10.2   14.33370
11          Cambridge  -71.0620  42.2236              21.5    1.65660
12 Boston East Boston  -71.0410  42.2290              10.9   15.87440
13             Newton  -71.1320  42.2142              29.0    0.44791
14          Cambridge  -71.0810  42.2368              17.4    1.20742
15    Boston Downtown  -71.0455  42.2060              27.5   14.43830
16    Boston Downtown  -71.0487  42.2048              17.2   14.05070
17             Newton  -71.1285  42.1930              31.7    0.46296
18          Cambridge  -71.0555  42.2222              14.6    2.36862
19    Boston Downtown  -71.0390  42.2198              11.9   20.71620
20          Cambridge  -71.0650  42.2223              23.3    1.42502
21          Cambridge  -71.0510  42.2205              11.8    2.77974
22          Cambridge  -71.0680  42.2150              15.6    3.53501
23             Newton  -71.1491  42.2030              31.5    0.51183
24             Newton  -71.1215  42.2025              37.6    0.38214
25          Cambridge  -71.0567  42.2240              17.8    2.33099
26             Newton  -71.1160  42.1947              31.6    0.41238
27          Cambridge  -71.0670  42.2245              24.3    1.34284
28          Cambridge  -71.0622  42.2205              19.6    1.49632
29 Boston East Boston  -71.0245  42.2235               8.8   20.08490
30             Newton  -71.1400  42.1946              41.7    0.57529
31             Newton  -71.1300  42.1880              24.3    0.53700
32             Newton  -71.1210  42.2166              21.7    0.40771
33          Cambridge  -71.0590  42.2170              15.3    1.12658
34    Boston Downtown  -71.0462  42.2075              15.0   51.13580
35          Cambridge  -71.0590  42.2210              15.6    2.15505
36          Cambridge  -71.0775  42.2351              22.3    2.44953
37             Newton  -71.1100  42.2137              26.7    0.35809
38 Boston East Boston  -71.0230  42.2287              11.3    9.18702
39 Boston East Boston  -71.0228  42.2231              10.5   24.39380
40    Boston Downtown  -71.0451  42.2015              16.3   28.65580
41          Cambridge  -71.0866  42.2345              23.8    1.80028
42 Boston East Boston  -71.0109  42.2300              15.1    6.96215
43          Cambridge  -71.0792  42.2390              19.1    2.31390
44             Newton  -71.1485  42.2110              25.1    0.52058
45          Cambridge  -71.0918  42.2265              22.7    2.24236
46 Boston East Boston  -71.0035  42.2330              23.2    5.29305
47          Cambridge  -71.0580  42.2230              15.4    2.73397
48             Newton  -71.1380  42.2141              24.0    0.33045
49             Newton  -71.1100  42.2060              44.8    0.31533
50 Boston East Boston  -71.0168  42.2281              11.5    8.15174
51          Cambridge  -71.0820  42.2295              25.0    2.92400
52          Cambridge  -71.0700  42.2214              27.0    1.27346
53          Cambridge  -71.0667  42.2200              13.1    2.44668
54    Boston Downtown  -71.0470  42.2030              17.9   18.81100
55             Newton  -71.1190  42.1807              31.5    0.44178
56          Cambridge  -71.0540  42.2190              13.8    2.37934
57             Newton  -71.1340  42.2040              48.3    0.33147
58 Boston East Boston  -71.0215  42.2248               7.4   22.59710
59    Boston Downtown  -71.0437  42.2050              17.2    7.40389
60 Boston East Boston  -71.0235  42.2213               7.2   16.81180
61             Newton  -71.1100  42.1850              46.7    0.29819
62             Newton  -71.1250  42.2134              27.5    0.62356
63          Cambridge  -71.0740  42.2331              23.8    2.30040
   zoned_25k_p indust_p borders_charles   NOx n_rooms_avg before_1940_p
1            0    18.10               0 0.700       5.520         100.0
2            0    19.58               1 0.871       5.403         100.0
3            0    18.10               0 0.659       5.608         100.0
4            0    19.58               1 0.871       6.129          96.0
5            0    18.10               0 0.700       5.036          97.0
6            0    19.58               0 0.871       5.709          98.5
7            0    19.58               0 0.605       6.943          97.4
8            0     6.20               0 0.507       6.618          80.8
9            0    19.58               0 0.871       5.468         100.0
10           0    18.10               0 0.700       4.880         100.0
11           0    19.58               0 0.871       6.122          97.3
12           0    18.10               0 0.671       6.545          99.1
13           0     6.20               1 0.507       6.726          66.5
14           0    19.58               0 0.605       5.875          94.6
15           0    18.10               0 0.597       6.852         100.0
16           0    18.10               0 0.597       6.657         100.0
17           0     6.20               0 0.504       7.412          76.9
18           0    19.58               0 0.871       4.926          95.7
19           0    18.10               0 0.659       4.138         100.0
20           0    19.58               0 0.871       6.510         100.0
21           0    19.58               0 0.871       4.903          97.8
22           0    19.58               1 0.871       6.152          82.6
23           0     6.20               0 0.507       7.358          71.6
24           0     6.20               0 0.504       8.040          86.5
25           0    19.58               0 0.871       5.186          93.8
26           0     6.20               0 0.504       7.163          79.9
27           0    19.58               0 0.605       6.066         100.0
28           0    19.58               0 0.871       5.404         100.0
29           0    18.10               0 0.700       4.368          91.2
30           0     6.20               0 0.507       8.337          73.3
31           0     6.20               0 0.504       5.981          68.1
32           0     6.20               1 0.507       6.164          91.3
33           0    19.58               1 0.871       5.012          88.0
34           0    18.10               0 0.597       5.757         100.0
35           0    19.58               0 0.871       5.628         100.0
36           0    19.58               0 0.605       6.402          95.2
37           0     6.20               1 0.507       6.951          88.5
38           0    18.10               0 0.700       5.536         100.0
39           0    18.10               0 0.700       4.652         100.0
40           0    18.10               0 0.597       5.155         100.0
41           0    19.58               0 0.605       5.877          79.2
42           0    18.10               0 0.700       5.713          97.0
43           0    19.58               0 0.605       5.880          97.3
44           0     6.20               1 0.507       6.631          76.5
45           0    19.58               0 0.605       5.854          91.8
46           0    18.10               0 0.700       6.051          82.5
47           0    19.58               0 0.871       5.597          94.9
48           0     6.20               0 0.507       6.086          61.5
49           0     6.20               0 0.504       8.266          78.3
50           0    18.10               0 0.700       5.390          98.9
51           0    19.58               0 0.605       6.101          93.0
52           0    19.58               1 0.605       6.250          92.6
53           0    19.58               0 0.871       5.272          94.0
54           0    18.10               0 0.597       4.628         100.0
55           0     6.20               0 0.504       6.552          21.4
56           0    19.58               0 0.871       6.130         100.0
57           0     6.20               0 0.507       8.247          70.4
58           0    18.10               0 0.700       5.000          89.5
59           0    18.10               0 0.597       5.617          97.9
60           0    18.10               0 0.700       5.277          98.1
61           0     6.20               0 0.504       7.686          17.0
62           0     6.20               1 0.507       6.879          77.7
63           0    19.58               0 0.605       6.319          96.1
   employ_dist radial_access tax_rate pupil_teacher_ratio lower_stat_pct
1       1.5331            24      666                20.2          24.56
2       1.3216             5      403                14.7          26.82
3       1.2852            24      666                20.2          12.13
4       1.7494             5      403                14.7          15.12
5       1.7700            24      666                20.2          25.68
6       1.6232             5      403                14.7          15.79
7       1.8773             5      403                14.7           4.59
8       3.2721             8      307                17.4           7.60
9       1.4118             5      403                14.7          26.42
10      1.5895            24      666                20.2          30.62
11      1.6180             5      403                14.7          14.10
12      1.5192            24      666                20.2          21.08
13      3.6519             8      307                17.4           8.05
14      2.4259             5      403                14.7          14.43
15      1.4655            24      666                20.2          19.78
16      1.5275            24      666                20.2          21.22
17      3.6715             8      307                17.4           5.25
18      1.4608             5      403                14.7          29.53
19      1.1781            24      666                20.2          23.34
20      1.7659             5      403                14.7           7.39
21      1.3459             5      403                14.7          29.29
22      1.7455             5      403                14.7          15.02
23      4.1480             8      307                17.4           4.73
24      3.2157             8      307                17.4           3.13
25      1.5296             5      403                14.7          28.32
26      3.2157             8      307                17.4           6.36
27      1.7573             5      403                14.7           6.43
28      1.5916             5      403                14.7          13.28
29      1.4395            24      666                20.2          30.63
30      3.8384             8      307                17.4           2.47
31      3.6715             8      307                17.4          11.65
32      3.0480             8      307                17.4          21.46
33      1.6102             5      403                14.7          12.12
34      1.4130            24      666                20.2          10.11
35      1.5166             5      403                14.7          16.65
36      2.2625             5      403                14.7          11.32
37      2.8617             8      307                17.4           9.71
38      1.5804            24      666                20.2          23.60
39      1.4672            24      666                20.2          28.28
40      1.5894            24      666                20.2          20.08
41      2.4259             5      403                14.7          12.14
42      1.9265            24      666                20.2          17.11
43      2.3887             5      403                14.7          12.03
44      4.1480             8      307                17.4           9.54
45      2.4220             5      403                14.7          11.64
46      2.1678            24      666                20.2          18.76
47      1.5257             5      403                14.7          21.45
48      3.6519             8      307                17.4          10.88
49      2.8944             8      307                17.4           4.14
50      1.7281            24      666                20.2          20.85
51      2.2834             5      403                14.7           9.81
52      1.7984             5      403                14.7           5.50
53      1.7364             5      403                14.7          16.14
54      1.5539            24      666                20.2          34.37
55      3.3751             8      307                17.4           3.76
56      1.4191             5      403                14.7          27.80
57      3.6519             8      307                17.4           3.95
58      1.5184            24      666                20.2          31.99
59      1.4547            24      666                20.2          26.40
60      1.4261            24      666                20.2          30.81
61      3.3751             8      307                17.4           3.92
62      3.2721             8      307                17.4           9.93
63      2.1000             5      403                14.7          11.10
   dist_fenway_park
1          9473.040
2          7084.501
3          7843.377
4          5835.269
5          9729.686
6          5983.767
7          5292.740
8          5311.258
9          6734.679
10         9696.166
11         5921.595
12         7563.394
13         6137.994
14         4350.347
15         7675.541
16         7441.357
17         6533.139
18         6459.483
19         7935.629
20         5742.059
21         6869.593
22         5754.337
23         7746.720
24         5848.785
25         6318.313
26         5855.101
27         5542.101
28         5991.314
29         9237.024
30         7250.903
31         6774.526
32         5375.525
33         6322.249
34         7581.210
35         6216.274
36         4580.270
37         4992.298
38         9296.364
39         9410.310
40         7816.928
41         4209.231
42        10493.650
43         4366.947
44         7506.759
45         4369.162
46        11213.265
47         6241.371
48         6581.485
49         5259.033
50         9924.656
51         4548.367
52         5437.980
53         5691.870
54         7624.081
55         6446.573
56         6660.058
57         6563.712
58         9509.525
59         7850.651
60         9372.921
61         5991.509
62         5704.143
63         4840.659
boxplot(crime_rate ~ town, data = Boston_census_new)

histogram(~ crime_rate | town, data = Boston_census_new,type = "percent")

favstats(~ crime_rate | town, data = Boston_census_new)
                town     min        Q1   median        Q3      max       mean
1    Boston Downtown 7.40389 13.525800 16.62465 22.701100 51.13580 20.8953488
2 Boston East Boston 5.29305  8.111925 12.95580 17.630075 24.39380 13.6050033
3          Cambridge 1.12658  1.442845  2.27138  2.448818  4.09740  2.1728142
4             Newton 0.29819  0.358090  0.44178  0.520580  0.62356  0.4453747
          sd  n missing
1 13.7822237  8       0
2  6.4193740 12       0
3  0.7706757 26       0
4  0.1045755 17       0
# Enligt histogram som vi skapade kan vi tydligt se att Boston Downtown har högre crime_rate än de resten grupperna. I och med enligt deskriptiv data som vi fick i figuren 3 där har Boston Downtown högst medelvärdet jämfört med de resten grupperna dvs vi kan dra ett beslut att Boston Downtown har en högre brottslighet än de resten grupperna.

💪 Uppgift 1.3

Vilka två variabler i datasetet Boston_census_data korrelerar mest med brottslighet? Beskriv sambandet mellan brottslighet och var och en av dessa två variabler.

Tip

Kom ihåg att korrelation mäter det linjära sambandet mellan numeriska variabler.

Uppgift 1.3 - Svar

Skriv svaret här.

suppressMessages(library(mosaic))
Boston_census_data_13_variables <- Boston_census_data[, c("longitude","latitude","median_home_value","crime_rate","zoned_25k_p","indust_p","NOx","n_rooms_avg","before_1940_p","employ_dist","pupil_teacher_ratio","lower_stat_pct","dist_fenway_park")]
head(Boston_census_data_13_variables)
  longitude latitude median_home_value crime_rate zoned_25k_p indust_p   NOx
1  -71.0677  42.2335              17.4    0.32264           0    21.89 0.624
2  -70.9650  42.1503              18.7    0.06151           0     5.19 0.515
3  -71.0215  42.2270              12.3    7.99248           0    18.10 0.700
4  -71.0511  42.1879              13.3    6.39312           0    18.10 0.584
5  -71.0455  42.1768              14.4    9.51363           0    18.10 0.713
6  -71.1095  42.3008              21.7    0.15876           0    10.81 0.413
  n_rooms_avg before_1940_p employ_dist pupil_teacher_ratio lower_stat_pct
1       5.942          93.5      1.9669                21.2          16.90
2       5.968          58.5      4.8122                20.2           9.29
3       5.520         100.0      1.5331                20.2          24.56
4       6.162          97.4      2.2060                20.2          24.10
5       6.728          94.1      2.4961                20.2          18.71
6       5.961          17.5      5.2873                19.2           9.88
  dist_fenway_park
1         5238.465
2        16343.799
3         9473.040
4         7692.103
5         8409.662
6         2137.660
correlation_matrix_Boston <- cor(Boston_census_data_13_variables)
#vi ser att variabel lower_stat_pct har en stark positiv korrelation ungefär 0,35 till crime_rate, variabel median_home_value har dock en stark negativ korrelation ungeför -0.45 till crime_rate.
round(correlation_matrix_Boston, 3)
                    longitude latitude median_home_value crime_rate zoned_25k_p
longitude               1.000    0.140            -0.326      0.056      -0.168
latitude                0.140    1.000             0.015     -0.092      -0.123
median_home_value      -0.326    0.015             1.000     -0.450       0.395
crime_rate              0.056   -0.092            -0.450      1.000      -0.196
zoned_25k_p            -0.168   -0.123             0.395     -0.196       1.000
indust_p                0.035   -0.063            -0.600      0.403      -0.522
NOx                     0.138   -0.085            -0.524      0.415      -0.506
n_rooms_avg            -0.227   -0.069             0.680     -0.213       0.299
before_1940_p           0.183    0.060            -0.488      0.350      -0.559
employ_dist             0.011   -0.069             0.368     -0.378       0.672
pupil_teacher_ratio     0.295   -0.002            -0.515      0.283      -0.375
lower_stat_pct          0.172    0.034            -0.765      0.464      -0.424
dist_fenway_park        0.435   -0.200            -0.003     -0.123       0.400
                    indust_p    NOx n_rooms_avg before_1940_p employ_dist
longitude              0.035  0.138      -0.227         0.183       0.011
latitude              -0.063 -0.085      -0.069         0.060      -0.069
median_home_value     -0.600 -0.524       0.680        -0.488       0.368
crime_rate             0.403  0.415      -0.213         0.350      -0.378
zoned_25k_p           -0.522 -0.506       0.299        -0.559       0.672
indust_p               1.000  0.761      -0.407         0.632      -0.706
NOx                    0.761  1.000      -0.315         0.725      -0.766
n_rooms_avg           -0.407 -0.315       1.000        -0.256       0.242
before_1940_p          0.632  0.725      -0.256         1.000      -0.744
employ_dist           -0.706 -0.766       0.242        -0.744       1.000
pupil_teacher_ratio    0.382  0.178      -0.289         0.264      -0.237
lower_stat_pct         0.640  0.615      -0.607         0.633      -0.544
dist_fenway_park      -0.394 -0.325       0.020        -0.304       0.686
                    pupil_teacher_ratio lower_stat_pct dist_fenway_park
longitude                         0.295          0.172            0.435
latitude                         -0.002          0.034           -0.200
median_home_value                -0.515         -0.765           -0.003
crime_rate                        0.283          0.464           -0.123
zoned_25k_p                      -0.375         -0.424            0.400
indust_p                          0.382          0.640           -0.394
NOx                               0.178          0.615           -0.325
n_rooms_avg                      -0.289         -0.607            0.020
before_1940_p                     0.264          0.633           -0.304
employ_dist                      -0.237         -0.544            0.686
pupil_teacher_ratio               1.000          0.364            0.043
lower_stat_pct                    0.364          1.000           -0.161
dist_fenway_park                  0.043         -0.161            1.000
suppressMessages(library(corrplot))
corrplot(correlation_matrix_Boston)

cor(lower_stat_pct ~ Crime_rate, data = Boston_census)
[1] 0.4637251
cor(median_home_value ~ Crime_rate, data = Boston_census)
[1] -0.4496238

2. Fastighetsskatt i Boston

I detta avsnitt ska ni analysera fastighetsskatten i Boston med hjälp av variabeln tax_rate.

💪 Uppgift 2.1

Vad kan man generellt säga om fastighetsskatten i distrikten? Använd lämpliga figurer och mått för att beskriva fördelningen.

Uppgift 2.1 - Svar

Skriv svaret här.

histogram(~tax_rate, data = Boston_census_data, main ="Fastighetsskatten i Boston", type ="count",col="navyblue")

favstats(~ tax_rate, data = Boston_census)
 min     Q1 median  Q3 max     mean       sd   n missing
 187 280.75    330 666 711 409.3271 168.5777 480       0
densityplot(~ tax_rate, data = Boston_census_data, col = "red")

💪 Uppgift 2.2

Låt oss skapa en ny variabel cat_tax som anger om ett distrikt betalar låg (low), medel (medium), eller hög (high) fastighetsskatt. Vi definerar skattekategorierna enligt

  • low: tax_rate \(\leq\) 250,
  • medium: 250 \(<\) tax_rate \(\leq\) 400,
  • high: tax_rate \(>\) 400.

Följande kod skapar och lägger till variabeln cat_tax i Boston_census_data

Boston_census_data$cat_tax <- cut(Boston_census_data$tax_rate, 
              breaks=c(0, 250, 400, 800),
              labels=c('Low', 'Medium', 'High'))

Finns det ett samband mellan vilken skattekategori ett distrikt tillhör och dess angränsning till Charles River? Förklara med hjälp av lämplig tabell och figur.

Uppgift 2.2 - Svar

Skriv svaret här.

tally(cat_tax ~ borders_charles, data = Boston_census_data, margins=TRUE, format="percent")
        borders_charles
cat_tax          0         1
  Low     13.30377  10.34483
  Medium  47.00665  55.17241
  High    39.68958  34.48276
  Total  100.00000 100.00000

💪 Uppgift 2.3

Hur många procent av alla distrikt i vår data ligger i angränsning till Charles River och tillhör en hög skattekategori? Hur stor andel av distrikten med hög skatt ligger inte i angränsning till Charles River?

Uppgift 2.3 - Svar

Skriv svaret här.

tally(borders_charles ~ cat_tax, data = Boston_census_data, margins=TRUE, format="percent")
               cat_tax
borders_charles        Low     Medium       High
          0      95.238095  92.982456  94.708995
          1       4.761905   7.017544   5.291005
          Total 100.000000 100.000000 100.000000

💪 Uppgift 2.4

Vilka två variabler i datasetet Boston_census_data korrelerar starkast med tax_rate? Beskriv det parvisa sambandet mellan tax_rate och var och en av dessa två variabler. Vad kan vi säga om kausalitet för vart och ett av sambanden?

Tip

Kom ihåg att korrelation är ett mått på linjära samband mellan numeriska variabler.

Uppgift 2.4 - Svar

Skriv svaret här.

suppressMessages(library(mosaic))
#vi ser att variabel lower_stat_pct har en stark positiv korrelation ungefär 0,35 till crime_rate, variabel median_home_value har dock en stark negativ korrelation ungeför -0.45 till crime_rate.
Boston_census_data_15_variables <- Boston_census_data[, c("longitude","latitude","median_home_value","crime_rate","zoned_25k_p","indust_p","NOx","n_rooms_avg","before_1940_p","employ_dist","radial_access","tax_rate","pupil_teacher_ratio","lower_stat_pct","dist_fenway_park")]
head(Boston_census_data_15_variables)
  longitude latitude median_home_value crime_rate zoned_25k_p indust_p   NOx
1  -71.0677  42.2335              17.4    0.32264           0    21.89 0.624
2  -70.9650  42.1503              18.7    0.06151           0     5.19 0.515
3  -71.0215  42.2270              12.3    7.99248           0    18.10 0.700
4  -71.0511  42.1879              13.3    6.39312           0    18.10 0.584
5  -71.0455  42.1768              14.4    9.51363           0    18.10 0.713
6  -71.1095  42.3008              21.7    0.15876           0    10.81 0.413
  n_rooms_avg before_1940_p employ_dist radial_access tax_rate
1       5.942          93.5      1.9669             4      437
2       5.968          58.5      4.8122             5      224
3       5.520         100.0      1.5331            24      666
4       6.162          97.4      2.2060            24      666
5       6.728          94.1      2.4961            24      666
6       5.961          17.5      5.2873             4      305
  pupil_teacher_ratio lower_stat_pct dist_fenway_park
1                21.2          16.90         5238.465
2                20.2           9.29        16343.799
3                20.2          24.56         9473.040
4                20.2          24.10         7692.103
5                20.2          18.71         8409.662
6                19.2           9.88         2137.660
correlation_matrix_Boston <- cor(Boston_census_data_15_variables)
round(correlation_matrix_Boston, 3)
                    longitude latitude median_home_value crime_rate zoned_25k_p
longitude               1.000    0.140            -0.326      0.056      -0.168
latitude                0.140    1.000             0.015     -0.092      -0.123
median_home_value      -0.326    0.015             1.000     -0.450       0.395
crime_rate              0.056   -0.092            -0.450      1.000      -0.196
zoned_25k_p            -0.168   -0.123             0.395     -0.196       1.000
indust_p                0.035   -0.063            -0.600      0.403      -0.522
NOx                     0.138   -0.085            -0.524      0.415      -0.506
n_rooms_avg            -0.227   -0.069             0.680     -0.213       0.299
before_1940_p           0.183    0.060            -0.488      0.350      -0.559
employ_dist             0.011   -0.069             0.368     -0.378       0.672
radial_access           0.015   -0.226            -0.479      0.623      -0.303
tax_rate                0.031   -0.189            -0.579      0.580      -0.300
pupil_teacher_ratio     0.295   -0.002            -0.515      0.283      -0.375
lower_stat_pct          0.172    0.034            -0.765      0.464      -0.424
dist_fenway_park        0.435   -0.200            -0.003     -0.123       0.400
                    indust_p    NOx n_rooms_avg before_1940_p employ_dist
longitude              0.035  0.138      -0.227         0.183       0.011
latitude              -0.063 -0.085      -0.069         0.060      -0.069
median_home_value     -0.600 -0.524       0.680        -0.488       0.368
crime_rate             0.403  0.415      -0.213         0.350      -0.378
zoned_25k_p           -0.522 -0.506       0.299        -0.559       0.672
indust_p               1.000  0.761      -0.407         0.632      -0.706
NOx                    0.761  1.000      -0.315         0.725      -0.766
n_rooms_avg           -0.407 -0.315       1.000        -0.256       0.242
before_1940_p          0.632  0.725      -0.256         1.000      -0.744
employ_dist           -0.706 -0.766       0.242        -0.744       1.000
radial_access          0.592  0.608      -0.190         0.447      -0.486
tax_rate               0.717  0.666      -0.278         0.499      -0.529
pupil_teacher_ratio    0.382  0.178      -0.289         0.264      -0.237
lower_stat_pct         0.640  0.615      -0.607         0.633      -0.544
dist_fenway_park      -0.394 -0.325       0.020        -0.304       0.686
                    radial_access tax_rate pupil_teacher_ratio lower_stat_pct
longitude                   0.015    0.031               0.295          0.172
latitude                   -0.226   -0.189              -0.002          0.034
median_home_value          -0.479   -0.579              -0.515         -0.765
crime_rate                  0.623    0.580               0.283          0.464
zoned_25k_p                -0.303   -0.300              -0.375         -0.424
indust_p                    0.592    0.717               0.382          0.640
NOx                         0.608    0.666               0.178          0.615
n_rooms_avg                -0.190   -0.278              -0.289         -0.607
before_1940_p               0.447    0.499               0.264          0.633
employ_dist                -0.486   -0.529              -0.237         -0.544
radial_access               1.000    0.910               0.453          0.513
tax_rate                    0.910    1.000               0.455          0.572
pupil_teacher_ratio         0.453    0.455               1.000          0.364
lower_stat_pct              0.513    0.572               0.364          1.000
dist_fenway_park           -0.206   -0.233               0.043         -0.161
                    dist_fenway_park
longitude                      0.435
latitude                      -0.200
median_home_value             -0.003
crime_rate                    -0.123
zoned_25k_p                    0.400
indust_p                      -0.394
NOx                           -0.325
n_rooms_avg                    0.020
before_1940_p                 -0.304
employ_dist                    0.686
radial_access                 -0.206
tax_rate                      -0.233
pupil_teacher_ratio            0.043
lower_stat_pct                -0.161
dist_fenway_park               1.000
corrplot(correlation_matrix_Boston)

cor(radial_access ~ tax_rate, data = Boston_census)
[1] 0.9099416
cor(indust_p ~ tax_rate, data = Boston_census)
[1] 0.7171041

3. Avstånd till Fenway park

I detta avsnitt ska ni undersöka variabeln dist_fenway_park, som mäter avståndet mellan ett distrikt och Fenway park (stadion där basebollslaget Boston Red Sox spelar sina hemmamatcher).

Vi kan visualisera Fenway park och distrikten på en karta med hjälp av R-paketet leaflet. Följande kod visar platsen för Fenway park och distrikten för observationerna 30 och 45.

library(leaflet) # Install if not available
fenway_park_lat_long <- c(42.346462, -71.097250) # latitude and longitude for Fenway_park
Boston_map <- leaflet() %>% 
  addTiles() %>%
  addMarkers(lat = fenway_park_lat_long[1], lng = fenway_park_lat_long[2], popup="Fenway park") %>%
  addMarkers(lat = Boston_census_data$latitude[30], lng = Boston_census_data$longitude[30], popup="Observation 30") %>%
  addMarkers(lat = Boston_census_data$latitude[45], lng = Boston_census_data$longitude[45], popup="Observation 45") 

Boston_map # Show interactive map

💪 Uppgift 3.1

Vilket distrikt i vår data har längst respektive kortast avstånd till Fenway park? Markera ut dessa distrikt i en interaktiv karta tillsammans med Fenway park.

Uppgift 3.1 - Svar

Skriv svaret här.

dist_fenway_sorted <- Boston_census_data %>% arrange(dist_fenway_park)
head(dist_fenway_sorted)
dist_fenway_sorted_hightolow <- Boston_census_data %>% arrange(desc(dist_fenway_park))
head(dist_fenway_sorted_hightolow)

library(leaflet) # Install if not available
fenway_park_lat_long <- c(42.346462, -71.097250) # latitude and longitude for Fenway_park
Boston_map <- leaflet() %>% 
  addTiles() %>%
  addMarkers(lat = fenway_park_lat_long[1], lng = fenway_park_lat_long[2], popup="Fenway park") %>%
  addMarkers(lat = dist_fenway_sorted$latitude[1], lng = dist_fenway_sorted$longitude[1], popup="kortast") %>%
  addMarkers(lat = dist_fenway_sorted_hightolow$latitude[1], lng = dist_fenway_sorted_hightolow$longitude[1], popup="Observation längst") 
Boston_map

💪 Uppgift 3.2

Finns det ett samband mellan dist_fenway_park och crime_rate?

Uppgift 3.2 - Svar

Skriv svaret här.

cor(dist_fenway_park ~ crime_rate, data = Boston_census_data)
[1] -0.1228651

4. Enkel linjär regression

I detta avsnitt ska ni anpassa och tolka enkla linjära regressionsmodeller.

💪 Uppgift 4.1

Anpassa en linjär regression med responsvariabeln NOx och den förklarande variabeln employ_dist. Rita den anpassade regressionslinjen tillsammans med data i en lämplig figur. Beskriv resultaten och tolka modellen. Utför en modellvalidering via en residualanalys och kommentera modellens lämplighet. Om modellen inte anses lämplig, vilka antaganden har inte varit uppfyllda?

Uppgift 4.1 - Svar

Skriv svaret här.

#Vi anpassar en enkel linjär regression med responsvariabel utandningsvolymen (NOx) och förklarande variabel längd (employdist) med hjälp av funktionen lm() som står för linear model och sparar resultatet i en variabel vi döper till lm_NOx_vs_employdist.
lm_NOx_vs_employdist <- lm(NOx ~ employ_dist, data = Boston_census)
lm_NOx_vs_employdist

Call:
lm(formula = NOx ~ employ_dist, data = Boston_census)

Coefficients:
(Intercept)  employ_dist  
    0.71761     -0.04264  
#En sådan funktion är summary() som skriver ut resultaten från regressionen i ett snyggt format.
summary(lm_NOx_vs_employdist)

Call:
lm(formula = NOx ~ employ_dist, data = Boston_census)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.12358 -0.05352 -0.01220  0.04348  0.22868 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.717614   0.007109  100.95   <2e-16 ***
employ_dist -0.042641   0.001639  -26.02   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.07526 on 478 degrees of freedom
Multiple R-squared:  0.5861,    Adjusted R-squared:  0.5852 
F-statistic: 676.9 on 1 and 478 DF,  p-value: < 2.2e-16
plot(NOx ~ employ_dist, data = Boston_census, col = "cornflowerblue", ylim = c(0, 1))
y_hat <- predict(lm_NOx_vs_employdist)
head(y_hat)
        1         2         3         4         5         6 
0.6337437 0.5124177 0.6522413 0.6235483 0.6111782 0.4921591 
lines(Boston_census$employ_dist, y_hat, type = "p", col = "lightcoral")
abline(lm_NOx_vs_employdist, col = "lightcoral")
legend(x = "topleft", pch = c(1, 1, NA), lty = c(NA, NA, 1), col = c("cornflowerblue", "lightcoral", "lightcoral"), legend=c("Data", "Predicted", "Fitted line"))

# residualer
resid <- residuals(lm_NOx_vs_employdist)
head(resid)
           1            2            3            4            5            6 
-0.009743748  0.002582251  0.047758653 -0.039548322  0.101821788 -0.079159083 
# residualanalys
plot(Boston_census$employ_dist, resid, xlab= "employ_dist", ylab='Residuals', col = "cornflowerblue") 

qqnorm(resid, col = "cornflowerblue") # Create normal probability plot for residuals
qqline(resid, col = "red") # Add a straight line to normal probability plot 

# Den är inte så slumpmässig, inte normalfördelad. 
# enkel linjär regression 

💪 Uppgift 4.2

Använd modellen i Uppgift 4.1 för att prediktera koncentration av kväveoxider för observation 10, där employ_dist=10.5857. Beräkna vad residualen blir för denna observation.

Uppgift 4.2 - Svar

Skriv svaret här.

new_x <- data.frame(employ_dist = c(10.5857))
predict(lm_NOx_vs_employdist, newdata = new_x)
        1 
0.2662308 

💪 Uppgift 4.3

Transformera variablerna i Uppgift 4.1 (avgör själv vilken eller vilka av de två som behöver transformeras). Ett förslag är att använda Tukeys cirkel för att hitta lämpliga transformationer. Anpassa en ny linjär regression med de transformerade variablerna. Utför en modellvalidering (efter transformation) via en residualanalys och kommentera modellens lämplighet jämfört med modellen i Uppgift 4.1.

Uppgift 4.3 - Svar

Skriv svaret här.

plot(NOx ~ employ_dist, data = Boston_census,col = "cornflowerblue") 

# Starting point: Both y and x  untransformed (Step 2 in the ladder of powers) 
plot(sqrt(NOx) ~ sqrt(employ_dist), data = Boston_census, col = "cornflowerblue")

# y down and x down in the ladder of powers
plot(log(NOx) ~ log(employ_dist), data = Boston_census, col = "cornflowerblue")

# y and x down two steps

lm_logNOx_vs_logemploy_dist <- lm(log(NOx) ~ log(employ_dist), data = Boston_census)
summary(lm_logNOx_vs_logemploy_dist)

Call:
lm(formula = log(NOx) ~ log(employ_dist), data = Boston_census)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.19152 -0.07828 -0.01370  0.06108  0.28496 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      -0.218492   0.011524  -18.96   <2e-16 ***
log(employ_dist) -0.327303   0.008832  -37.06   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.103 on 478 degrees of freedom
Multiple R-squared:  0.7418,    Adjusted R-squared:  0.7413 
F-statistic:  1373 on 1 and 478 DF,  p-value: < 2.2e-16
logy_hat <- predict(lm_logNOx_vs_logemploy_dist) # log scale prediction
y_hat <- exp(logy_hat) # original scale prediction
head(logy_hat)
         1          2          3          4          5          6 
-0.4398989 -0.7327355 -0.3583458 -0.4774478 -0.5178857 -0.7635522 
head(y_hat)
        1         2         3         4         5         6 
0.6441015 0.4805925 0.6988314 0.6203647 0.5957789 0.4660081 
plot(NOx ~ employ_dist, data = Boston_census, col = "cornflowerblue", ylim = c(0, 7)) # Data on original scale
lines(Boston_census$employ_dist, y_hat, type = "p", col = "lightcoral")
abline(lm_logNOx_vs_logemploy_dist, col = "lightcoral")
legend(x = "topleft", pch = c(0,5, 0,5, NA), lty = c(NA, NA, 0,5), col = c("cornflowerblue", "lightcoral", "lightcoral"), legend=c("Data", "Predicted", "Fitted line"))

💪 Uppgift 4.4

Plotta den anpassade regressionen från 4.3 i icke-transformerad skala tillsammans med observationerna (också i icke-transformerad skala) i en lämplig figur.

Uppgift 4.4 - Svar

Skriv svaret här.

# Write your code here

💪 Uppgift 4.5

Använd modellen i Uppgift 4.3 för att prediktera koncentration av kväveoxider i icke-transformerad skala för observation 10, där employ_dist=10.5857. Beräkna vad residualen blir för denna observation. Kommentera resultaten jämfört med Uppgift 4.2.

Tip

Tänk på att ta hänsyn till eventuella transformationer!

Uppgift 4.5 - Svar

Skriv svaret här.

# Write your code here

5. Multipel linjär regression

I detta avsnitt ska ni studera multipel linjära regression.

💪 Uppgift 5.1

Anpassa en linjär regression med responsvariabel logaritmerad median_home_value samt förklarande variabler lower_stat_pct och dummy-variabeln borders_charles. Tolka koefficienten för borders_charles.

Uppgift 5.1 - Svar

Skriv svaret här.

lm_median_home_value_vs_lower_stat_pct_borders_charles <- lm(median_home_value ~ lower_stat_pct + borders_charles, data = Boston_census)
summary(lm_median_home_value_vs_lower_stat_pct_borders_charles)

Call:
lm(formula = median_home_value ~ lower_stat_pct + borders_charles, 
    data = Boston_census)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.2067 -3.1683 -0.9976  1.6929 21.4235 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)     32.36661    0.48051  67.358   <2e-16 ***
lower_stat_pct  -0.84435    0.03231 -26.130   <2e-16 ***
borders_charles  2.37058    0.95755   2.476   0.0136 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.998 on 477 degrees of freedom
Multiple R-squared:  0.5912,    Adjusted R-squared:  0.5895 
F-statistic:   345 on 2 and 477 DF,  p-value: < 2.2e-16
resid_median_multiplereg <- residuals(lm_median_home_value_vs_lower_stat_pct_borders_charles)
head(resid_median_multiplereg)
         1          2          3          4          5          6 
-0.6971156 -5.8226098  0.6705960  1.2821955 -2.1688443 -2.3244440 
plot(lm_median_home_value_vs_lower_stat_pct_borders_charles$fitted.values, resid_median_multiplereg, xlab= "y_hat", ylab='Residuals', col = "cornflowerblue") 

qqnorm(resid_median_multiplereg, col = "cornflowerblue") # Create normal probability plot for residuals
qqline(resid_median_multiplereg, col = "red") # Add a straight line to normal

💪 Uppgift 5.2

Ni ska nu utforma en modell som predikterar medianhuspriset median_home_value. Ni får endast använda följande förklaringsvariabler:

  • before_1940_p
  • crime_rate
  • radial_access
  • NOx
  • dist_fenway_park

Ni får själva välja hur många av variablerna som ska ingå i modellen. Ni får göra vilka transformationer ni vill av variablerna, inklusive responsvariabeln.

Pröva er fram metodiskt när ni väljer vilka variabler ni inkluderar i modellen, och när ni bestämmer vilka eventuella transformationer ni använder.

När ni utvärderar olika modeller kan ni förslagsvis börja med att jämföra adjusted R-squared. När ni med hjälp av adjusted R-squared har identifierat två eller tre modeller som ser lovande ut kan ni utvärdera dessa modeller ytterligare i ett andra steg.

I det andra steget ska ni utvärdera hur väl modellerna predikterar data som inte använts för att anpassa modellen. Ni kan välja en av två alternativa metoder:

  1. Dela in ert dataset i träningsdata och testdata. Anpassa modellen med hjälp av träningsdata, och utvärdera sedan på testdata. Ni kan exempelvis använda de första 350 observationerna som träningsdata och de sista 130 observationerna som testdata.
  2. Använd korsvalidering. Det är en något mer krävande metod, men också något bättre. Ni kan exempelvis göra korsvalidering med 4 folds (4-fold cross validation). Dela då upp ert dataset i fyra delar (del 1: observationer 1-120, del 2: observationer 121-240, del 3: observationer 241-360, del 4: observationer 361-480).

Sortera inte observationerna i Boston_census_data slumpmässigt. Ordningen är redan slumpmässig.

Tip

Tänk på att ta hänsyn till eventuell transformation av responsvariabeln. Om ni exempelvis har valt transformationen \(\log(y)\) är modellens prediktion av responsvariabeln \(\widehat{\log(y)}\). Ni måste då transformera den till \(\hat y\) i responsvariabelns originalskala med formeln \(\hat{y}=\exp\left(\widehat{\log(y)}\right)\). Sedan kan ni räkna ut residualen \(y - \hat y\).

Uppgift 5.2 - Svar

Skriv svaret här

plot(median_home_value ~ before_1940_p + NOx, data = Boston_census, col = "cornflowerblue")

# Write your code here

💪 Uppgift 5.3

Gör en residualanalys av den valda modellen i Uppgift 5.2.

Uppgift 5.3 - Svar

Skriv svaret här.

# Write your code here

💪 Uppgift 5.4

Använd modellen i Uppgift 5.2 för att prediktera medianhuspriset för observationerna i datasetet Boston_districts_to_predict (ladda ner).

Uppgift 5.4 - Ladda hem data för prediktion

Ladda in dataseten Boston_districts_to_predict med följande kod.

# Write your code here
load(file = url("https://github.com/StatisticsSU/SDA1/blob/main/assignments/assignment1/Boston_districts_to_predict.RData?raw=true")) 

Det här datasetet har endast de förklarande variablerna, dvs inte responsvariabeln. När vi rättar era inlämningsuppgifter kommer vi att jämföra era prediktioner med de faktiska medianpriserna (som vi har tillgång till).

Skriv ut dina prediktioner så att vi enkelt kan se dem när vi rättar.

Tip

Tänk på att ta hänsyn till eventuella transformationer av förklaringsvariablerna!

Uppgift 5.4 - Svar

Skriv svaret här.

# Write your code here

Footnotes

  1. Totalundersökningen trunkerade medianhusvärdet till 50K för de censusdistrikten som låg över. Vi har tagit bort dessa censusdistrikt. Vi har också tagit bort variabler som är irrelevanta.↩︎

  2. Harrison Jr, D., & Rubinfeld, D. L. (1978). Hedonic housing prices and the demand for clean air. Journal of Environmental Economics and Management, 5(1), 81-102.↩︎

  3. Pace, R. K., & Gilley, O. W. (1997). Using the spatial configuration of the data to improve estimation. The Journal of Real Estate Finance and Economics, 14(3), 333-340.↩︎